Stats Exam 1 review

We have strong evidence that Sarah is not simply guessing, since 7 out 8 rarely occurs by chance (if just guessing).

A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the problem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the correct photo depicting a solution to the problem. Sarah chose the correct photo in seven of eight scenarios that she was presented.We want to run a test of significance to determine whether Sarah understands how to solve problems and will thus pick the photo of the correct solution more often than what would be done by random chance. Based on the p-value, what can be said about Sarah's ability to understand how to solve problems similar to those she was presented? We have strong evidence that Sarah is not simply guessing, since 7 out 8 rarely occurs by chance (if just guessing). We have no evidence that Sarah is not simply guessing, since 7 out 8 commonly occurs (if just guessing). We have strong evidence that Sarah is simply guessing, since 7 out 8 occurs every time (if just guessing). We have less evidence that Sarah is simply guessing, since 7 out 8 always occurs by chance (if just guessing).

long run proportion 0.875

A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the problem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the correct photo depicting a solution to the problem. Sarah chose the correct photo in seven of eight scenarios that she was presented.We want to run a test of significance to determine whether Sarah understands how to solve problems and will thus pick the photo of the correct solution more often than what would be done by random chance. The symbol π in this context stands for the ______________ of times that Sarah chooses the correct photo What is the observed value of the statistic in this case? (Round your answer to 3 decimal places; e.g. 5.275.)

Since 4 of the 100 simulated outcomes gave a result of 7 or more, the p-value is 0.04.

A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the problem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the correct photo depicting a solution to the problem. Sarah chose the correct photo in seven of eight scenarios that she was presented.We want to run a test of significance to determine whether Sarah understands how to solve problems and will thus pick the photo of the correct solution more often than what would be done by random chance. We conducted a test of significance using the One Proportion applet and got the following null distribution for the "number of heads." Based on the null distribution, what is the p-value for the test?How did you calculate it? ​Probability of heads: 0.5Number of tosses: 8Number of repetitions: 100Total = 100 Since 96 of the 100 simulated outcomes gave a result less than 7, the probability she would get less than 7 correct out of 8 is 0.04. Since 32 of the 100 simulated outcomes gave the most common result of 4, the p-value is 0.32. Since 3 of the 100 simulated outcomes gave a result of 7, the p-value is 0.03. Since 4 of the 100 simulated outcomes gave a result of 7 or more, the p-value is 0.04.

the proportion of the time that Sarah would choose the correct picture (out of 8) if she were just guessing

A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the problem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the correct photo depicting a solution to the problem. Sarah chose the correct photo in seven of eight scenarios that she was presented.We want to run a test of significance to determine whether Sarah understands how to solve problems and will thus pick the photo of the correct solution more often than what would be done by random chance. What does a single dot in the null distributon represent in terms of Sarah and the photos? the proportion of the time that Sarah would choose the correct picture (out of 8) if she were just guessing the number of times Sarah would choose the correct picture (out of 8) if she were just guessing the proportion of the time that Sarah would choose the correct picture (out of 8) if she understood how to solve problems the number of times Sarah would choose the correct picture (out of 8) if she understood how to solve problems

If Sarah doesn't understand how to solve problems and is just guessing at which picture to select, the probability she would get 7 or more correct out of 8 is 0.04.

A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the problem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the correct photo depicting a solution to the problem. Sarah chose the correct photo in seven of eight scenarios that she was presented.We want to run a test of significance to determine whether Sarah understands how to solve problems and will thus pick the photo of the correct solution more often than what would be done by random chance. Which of the following best describes the meaning of the p-value in this situation? If Sarah understands how to solve problems and is not just guessing at which picture to select, the probability she would get 5 or more correct out of 8 is 0.04. If Sarah doesn't understand how to solve problems and is just guessing at which picture to select, the probability she would get 7 or more correct out of 8 is 0.04. If Sarah understands how to solve problems and is not just guessing at which picture to select, the probability she would get 7 or more correct out of 8 is 0.04. If Sarah doesn't understand how to solve problems and is randomly choosing which picture to select, the probability she would get less than 7 correct out of 8 is 0.04.

Null: The long-run proportion of times Sarah chooses the correct photo is 0.5; H0: π= 0.5​Alt: The long-run proportion of times Sarah chooses the correct photo is more than 0.5; Ha: π > 0.5

A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the problem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the correct photo depicting a solution to the problem. Sarah chose the correct photo in seven of eight scenarios that she was presented.We want to run a test of significance to determine whether Sarah understands how to solve problems and will thus pick the photo of the correct solution more often than what would be done by random chance. Which of the following represents the null and alternative hypotheses? Null: The long-run proportion of times Sarah chooses the incorrect photo is 0.5; H0: π= 0.5​Alt: The long-run proportion of times Sarah chooses the incorrect photo is more than 0.5; Ha: π>0 Null: The long-run proportion of times Sarah chooses the correct photo is 0.5; H0: π= 0.5​Alt: The long-run proportion of times Sarah chooses the correct photo is more than 0.5; Ha: π > 0.5 Null: The long-run proportion of times Sarah chooses the correct photo is less than 0.5; H0: π < 0.5​Alt: The long-run proportion of times Sarah chooses the correct photo is 0.5; Ha: π = 0.5 Null: The long-run proportion of times Sarah chooses the correct photo is less than 0.5; H0: π< 0.5​Alt: The long-run proportion of times Sarah chooses the correct photo is more than 0.5; Ha: π > 0.5

If she were guessing she'd rarely get 8 out of 8 correct.

A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups. Based on your simulation analysis, select the statement that produces strong evidence that the woman is not guessing as to whether milk or tea was poured first. If she were guessing she'd rarely get 8 out of 8 correct. If she were guessing she'd certainly get 8 out of 8 correct. If she were guessing she'd definitely get 8 out of 8 correct. If she were guessing she'd never get 8 out of 8 correct.

unlikely

A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups. Now use the One Proportion applet to simulate the outcomes of the woman guessing which was poured first for eight cups and repeat this 1000 times. Based on the applet's result, getting 8 out of 8 results correct would be ________________ to occur just by chance

Repeat the process many times (1000). If 8 correct out of 8 cups rarely occurs, then it is unlikely that the woman was just guessing as to what was poured first.

A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups. Suppose tossing a coin 8 times represents the 8 cups of tea, heads represents a correct identification of what was poured first, tea or milk, and tails represents an incorrect identification of what was poured first. Select the best conclusion you would draw about whether the woman was just guessing. Repeat the process many times (1000). If 4 correct out of 8 cups rarely occurs, then it is unlikely that the woman was just guessing as to what was poured first. Repeat the process many times (1000). If 6 correct out of 8 cups rarely occurs, then it is most likely that the woman was just guessing as to what was poured first. Repeat the process many times (1000). If 8 correct out of 8 cups rarely occurs, then it is likely that the woman was just guessing as to what was poured first. Repeat the process many times (1000). If 8 correct out of 8 cups rarely occurs, then it is unlikely that the woman was just guessing as to what was poured first.

True

A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups. The result obtained is statistically significant that she is not guessing as she gets 8 out of 8 correct. True False

True False

A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups.​ It is possible that the woman could get all eight correct if she were randomly guessing with each cup. True False It is likely that the woman could get all eight correct if she were randomly guessing with each cup. True False

The observational units are the eight cups and the variable is if she correctly identified which was poured first or not.

A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups.​ What are the observational units and variable in this study? The observational unit is the woman and the variable is if she correctly identified which was poured first or not. The observational units are whether tea or milk was added first and the variable is the woman. The observational units are the eight cups and the variable is if she correctly identified which was poured first or not. The observational units are the eight cups and the variable is the woman.

sample size=8, p^=0.5

A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups.​ What are the sample size and observed value of the statistic for this study? sample size=16, p^=1.0 sample size=8, p^=1.0 sample size=8, p^=0.5 sample size=16, p^=0.5

the long-run proportion of times the woman correctly identifies a cup

A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups.​ What is the parameter for this study? whether the tea or milk was poured first the proportion of times in eight tries the woman correctly identified a cup the long-run proportion of tea added first to the cup the long-run proportion of times the woman correctly identifies a cup

A type I error is possible here

A famous study from the 1960s explored whether two dolphins (Doris and Buzz) could communicate abstract ideas. Researchers believed dolphins could communicate simple feelings like "Watch out!" or "I'm happy," but Dr. Jarvis Bastian wanted to explore whether they could also communicate in a more abstract way, much like humans do. To investigate this, Dr. Bastian spent many years training Doris and Buzz and exploring the limits of their communicative ability.During a training period lasting many months, Dr. Bastian placed buttons underwater on each end of a large pool—two buttons for Doris and two buttons for Buzz. He then used an old automobile headlight as his signal. When he turned on the headlight and let it shine steadily, he intended for this signal to mean "push the button on the right." When he let the headlight blink on and off, this was meant as a signal to "push the button on the left." Every time the dolphins pushed the correct button, Dr. Bastian gave the dolphins a reward of some fish. Over time Doris and Buzz caught on and could earn their fish reward every time.Then Dr. Bastian made things a bit harder. Now, Buzz had to push his button before Doris. If they didn't push the buttons in the correct order—no fish. After a bit more training, the dolphins caught on again and could earn their fish reward every time. The dolphins were now ready to participate in the real study to examine whether they could communicate with each other.Dr. Bastian placed a large canvas curtain in the middle of the pool. Doris was on one side of the curtain and could see the headlight, whereas Buzz was on the other side of the curtain and could not see the headlight. Dr. Bastian turned on the headlight and let it shine steadily. He then watched to see what Doris would do. After looking at the light, Doris swam near the curtain and began to whistle loudly. Shortly after that, Buzz whistled back and then pressed the button on the right—he got it correct and so both dolphins got a fi sh. But this single attempt was not enough to convince Dr. Bastian that Doris had communicated with Buzz through her whistling. Dr. Bastian repeated the process several times, sometimes having the light blink (so Doris needed to let Buzz know to push the left button) and other times having it glow steadily (so Doris needed to let Buzz know to push the right button). He kept track of how often Buzz pushed the correct button. In doing so, we tested whether Buzz, one of the dolphins, could push the correct button more than 50% of the time in the long run. We found that the observed data provided very strong evidence that Doris and Buzz were actually communicating better than random chance. Which type of error (I or II) could we possibly be making with this conclusion?

Buzz is guessing, but we determine that he is not guessing Buzz is not guessing, but we do not determine that he is not guessing

A famous study from the 1960s explored whether two dolphins (Doris and Buzz) could communicate abstract ideas. Researchers believed dolphins could communicate simple feelings like "Watch out!" or "I'm happy," but Dr. Jarvis Bastian wanted to explore whether they could also communicate in a more abstract way, much like humans do. To investigate this, Dr. Bastian spent many years training Doris and Buzz and exploring the limits of their communicative ability.During a training period lasting many months, Dr. Bastian placed buttons underwater on each end of a large pool—two buttons for Doris and two buttons for Buzz. He then used an old automobile headlight as his signal. When he turned on the headlight and let it shine steadily, he intended for this signal to mean "push the button on the right." When he let the headlight blink on and off, this was meant as a signal to "push the button on the left." Every time the dolphins pushed the correct button, Dr. Bastian gave the dolphins a reward of some fish. Over time Doris and Buzz caught on and could earn their fish reward every time.Then Dr. Bastian made things a bit harder. Now, Buzz had to push his button before Doris. If they didn't push the buttons in the correct order—no fish. After a bit more training, the dolphins caught on again and could earn their fish reward every time. The dolphins were now ready to participate in the real study to examine whether they could communicate with each other.Dr. Bastian placed a large canvas curtain in the middle of the pool. Doris was on one side of the curtain and could see the headlight, whereas Buzz was on the other side of the curtain and could not see the headlight. Dr. Bastian turned on the headlight and let it shine steadily. He then watched to see what Doris would do. After looking at the light, Doris swam near the curtain and began to whistle loudly. Shortly after that, Buzz whistled back and then pressed the button on the right—he got it correct and so both dolphins got a fish. But this single attempt was not enough to convince Dr. Bastian that Doris had communicated with Buzz through her whistling. Dr. Bastian repeated the process several times, sometimes having the light blink (so Doris needed to let Buzz know to push the left button) and other times having it glow steadily (so Doris needed to let Buzz know to push the right button). He kept track of how often Buzz pushed the correct button.In doing so, we tested whether Buzz, one of the dolphins, could push the correct button more than 50% of the time in the long run. Describe what a Type I error would be in this study. Describe what a Type II error would be in this study.

Observational units are the couples; the variable is whether the male or female said I love you first; categorical

A recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. The researchers interviewed 96 university students that had been or were currently involved in a romantic heterosexual relationship where at least one person said "I love you." The students were asked, "Think about your last or current romantic relationship in which someone confessed their love. In this relationship, who admitted love first?"​ Previous studies have suggested that males tend to say "I love you" first. Identify the observational units and variable in this study. Also classify the variable as categorical or quantitative.

59/96 = 0.61 is the sample proportion; we use the symbol p-hat to denote this quantity.

A recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. The researchers interviewed 96 university students that had been or were currently involved in a romantic heterosexual relationship where at least one person said "I love you." The students were asked, "Think about your last or current romantic relationship in which someone confessed their love. In this relationship, who admitted love first?"​ Previous studies have suggested that males tend to say "I love you" first. It turned out that for 59 of the 96 responses, the man said "I love you" before the woman did.What is the sample proportion of couples for whom the man was the first to say "I love you" and what symbol do we use to denote this proportion? 59/96 = 0.61 is the sample proportion; we use the symbol π to denote this quantity. 59/96 = 0.61 is the sample proportion; we use the symbol p-hat to denote this quantity. 96/59 = 1.63 is the sample proportion; we use the symbol π to denote this quantity. 96/59 = 1.63 is the sample proportion; we use the symbol p-hat to denote this quantity.

True Strong

A recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. The researchers interviewed 96 university students that had been or were currently involved in a romantic heterosexual relationship where at least one person said "I love you." The students were asked, "Think about your last or current romantic relationship in which someone confessed their love. In this relationship, who admitted love first?"​ Previous studies have suggested that males tend to say "I love you" first. The p-value in this scenario is the probability of observing the proportion 0.61 or larger assuming the null hypothesis is We have ____________ evidence that the long-run proportion of university student relationships in which the man says "I love you" first is more than 50%.

96

A recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. The researchers interviewed 96 university students that had been or were currently involved in a romantic heterosexual relationship where at least one person said "I love you." The students were asked, "Think about your last or current romantic relationship in which someone confessed their love. In this relationship, who admitted love first?"​ Previous studies have suggested that males tend to say "I love you" first. To use a coin-flipping model to find the p-value for these data, flip a coin ____________ times and keep track of the number of heads. Repeat this process many times, keeping track of the number of heads each time.

probability of heads: 0.5, number of tosses: 96, number of repetitions: 1000, as extreme as ≥ 0.61; yields a p-value of approximately 0.016

A recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. The researchers interviewed 96 university students that had been or were currently involved in a romantic heterosexual relationship where at least one person said "I love you." The students were asked, "Think about your last or current romantic relationship in which someone confessed their love. In this relationship, who admitted love first?"​ Previous studies have suggested that males tend to say "I love you" first. Use an applet to conduct a simulation analysis to assess the strength of evidence against the null hypothesis. Which p-value is the most valid? probability of heads: 0.61, number of tosses: 96, number of repetitions: 1000, as extreme as ≥ 0.61; yields a p-value of approximately 0.016 probability of heads: 0.61, number of tosses: 96, number of repetitions: 1000, as extreme as ≥ 0.61; yields a p-value of approximately 0.5 probability of heads: 0.5, number of tosses: 96, number of repetitions: 1000, as extreme as ≥ 0.61; yields a p-value of approximately 0.016 probability of heads: 0.5, number of tosses: 96, number of repetitions: 1000, as extreme as ≥ 0.61; yields a p-value of approximately 0.5

Null: The proportion of all couples where the male said "I love you" first is 0.50.Alt: The proportion of all couples where the male said "I love you" first is greater than 0.50

A recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. The researchers interviewed 96 university students that had been or were currently involved in a romantic heterosexual relationship where at least one person said "I love you." The students were asked, "Think about your last or current romantic relationship in which someone confessed their love. In this relationship, who admitted love first?"​ Previous studies have suggested that males tend to say "I love you" first. Which of the following describes the best null and alternative hypotheses? Null: The proportion of all couples where the female said "I love you" first is 0.50.Alt: The proportion of all couples where the female said "I love you" first is greater than 0.50 Null: The proportion of all couples where the female said "I love you" first is 0.50.Alt: The proportion of all couples where the male said "I love you" first is less than 0.50 Null: The proportion of all couples where the male said "I love you" first is 0.50.Alt: The proportion of all couples where the male said "I love you" first is greater than 0.50 Null: The proportion of all couples where the male said "I love you" first is 0.50.Alt: The proportion of all couples where the male said "I love you" first is less than 0.50

The variable is the time spent reading or watching news coverage Quantitative

A television news program has been running a story on a recent criminal trial. The news program invites viewers to go to their website and take a survey. One of the questions asks participants to report the amount of time the respondent spent reading or watching the news coverage about the trial during the last three days. The poll found that, on average, respondents had spent 92 minutes reading or watching news coverage about the trial during the last three days. Identify the variable measured on each respondent. The poll found that, on average, respondents had spent 92 minutes reading or watching news coverage about the trial during the last three days. Is the variable categorical or quantitative?

dot plot

A television news program has been running a story on a recent criminal trial. The news program invites viewers to go to their website and take a survey. One of the questions asks participants to report the amount of time the respondent spent reading or watching the news coverage about the trial during the last three days. The poll found that, on average, respondents had spent 92 minutes reading or watching news coverage about the trial during the last three days. The poll found that, on average, respondents had spent 92 minutes reading or watching news coverage about the trial during the last three days. Identify one graph that the news program could use to summarize the variable. Line graph Dot plot Regression graph Scatter plot

mean or median

A television news program has been running a story on a recent criminal trial. The news program invites viewers to go to their website and take a survey. One of the questions asks participants to report the amount of time the respondent spent reading or watching the news coverage about the trial during the last three days. The poll found that, on average, respondents had spent 92 minutes reading or watching news coverage about the trial during the last three days. The poll found that, on average, respondents had spent 92 minutes reading or watching news coverage about the trial during the last three days. Identify two statistics that the news program could use to summarize the variable. Mean or Median Median or proportion Mean or Mode Mean or Proportion

The variable of interst is the number of hours spent watching television per day and it is quantitative mu = the average number of hours spent watching television per day for all CalPoly students. H_0: mu= 2.75, H_a: mu (does not equal sign) 2.75

According to a 2011 report by the U.S. Department of Labor, civilian Americans spend 2.75 hours per day watching television. A faculty researcher, Dr. Sameer, at California Polytechnic State University (Cal Poly) conducts a study to see whether a different average applies to Cal Poly students.​ Identify the variable of interest and whether the variable is categorical or quantitative. Describe Dr. Sameer's parameter of interest and assign an appropriate symbol to denote it. Write the appropriate hypotheses using symbols.

Since this is a one-sided test, Dr. Elliot's p-value should be about half that of Dr. Sameer's.

According to a 2011 report by the U.S. Department of Labor, civilian Americans spend 2.75 hours per day watching television. A faculty researcher, Dr. Sameer, at California Polytechnic State University (Cal Poly) conducts a study to see whether a different average applies to Cal Poly students.​ Reconsider Dr. Sameer's research question about how much time Cal Poly students spend on watching television. Another faculty researcher, Dr. Elliot, had hypothesized that Cal Poly students spend more than 2.75 hours/day watching TV, on average. If Dr. Elliot were to use the same data as Dr. Sameer to conduct an investigation, how, if at all, would this researcher's p-value compare to the p-value reported in (a)? Explain how you are deciding. Since this is a one-sided test, Dr. Elliot's p-value should be bigger than that of Dr. Sameer's. Since this is a one-sided test, Dr. Elliot's p-value should be smaller than that of Dr. Sameer's. Since this is a one-sided test, Dr. Elliot's p-value should be same than that of Dr. Sameer's. Since this is a one-sided test, Dr. Elliot's p-value should be about half that of Dr. Sameer's.

If the mean daily TV watching time for Cal Poly students is 2.75 hours, the probability we would get a sample mean as extreme as 3.01 from a random sample of 100 students is 0.16.

According to a 2011 report by the U.S. Department of Labor, civilian Americans spend 2.75 hours per day watching television. A faculty researcher, Dr. Sameer, at California Polytechnic State University (Cal Poly) conducts a study to see whether a different average applies to Cal Poly students.​ Reconsider Dr. Sameer's research question about how much time Cal Poly students spend on watching television. Suppose that on analyzing the data from the survey of a random sample of 100 Cal Poly students, the p-value for Dr. Sameer's study was computed to be 0.16. Interpret what this p-value means in the context of the study. If the mean daily TV watching time for Cal Poly students is 2.75 hours, the probability we would get a sample mean greater than 3.01 from a random sample of 100 students is 0.16. If the mean daily TV watching time for Cal Poly students is 2.75 hours, the probability we would get a sample mean as extreme as 3.01 from a random sample of 100 students is 0.16. If the mean daily TV watching time for Cal Poly students is 2.75 hours, the probability we would get a sample mean less than 3.01 from a random sample of 100 students is 0.16. If the mean daily TV watching time for Cal Poly students is 2.75 hours, the probability we would not get a sample mean as extreme as 3.01 from a random sample of 100 students is 0.16.

If you repeatedly draw M&Ms at random a very large number of times, in the long-run 20% of those M&Ms will be red.

Answer this question for each of the following statements: Which of the following explains what it means to say "the probability of ..." while describing the random process that is repeated over and over again? The probability of getting a red M&M candy is 0.2. If you repeatedly draw M&Ms at random a very large number of times, in the long-run 20% of those M&Ms will be red. Each time you draw ten M&Ms, two of the M&Ms should be red. For every 100 M&Ms, there should be 20 M&Ms in the bag of candies. All of these are correct interpretations of probability.

true true gender of the child, binary do both parents smoke, two

Are newborns from couples where both parents smoke less likely to be boys than newborns from couples where neither parent smokes? Answer each of the following questions. In the question "Are newborns from couples where both parents smoke less likely to be boys than newborns from couples where neither parent smokes?" the observational units are newborns. In this question "Are newborns from couples where both parents smoke less likely to be boys than newborns from couples where neither parent smokes?", the variables are the gender of the baby and whether or not both parents smoke. In this question "Are newborns from couples where both parents smoke less likely to be boys than newborns from couples where neither parent smokes?"____________ is a categorical variable that is __________ In this question "Are newborns from couples where both parents smoke less likely to be boys than newborns from couples where neither parent smokes?" ______________ is a categorical variable that has ________ possible outcomes

The patient does not have the disease, but the test says the patient has the disease The patient has the disease, but the test says the patient is healthy Type II

As with a jury trial, another analogy to hypothesis testing involves medical diagnostic tests. These tests aim to indicate whether or not the patient has a particular disease. But the tests are not infallible, so errors can be made. The null hypothesis can be regarded as the patient being healthy. The alternative hypothesis can be regarded as the patient having the disease. Describe what Type I error represents in this situation.Deciding the Describe what Type II error represents in this situation. What type of error would you consider to be more serious (i.e. could lead to a more disastrous outcome)?

was there a death on the shift, and did Kristin Gilbert work the shift

Consider the scenario: "Statistical evidence was used in the murder trial of Kristen Gilbert, a nurse who was accused of killing patients. More than 1,000 eight-hour shifts were analyzed. Was the proportion of shifts with a death substantially higher for the shifts that Gilbert worked?​" The categorical variable(s) in this scenario is/are: was there a death on the shift, and did Kristin Gilbert work the shift was there a death on the shift did Kristin Gilbert work the shift none of these choices are correct.

The true, long-run average needle diameter (mu) Null: (mu = 1.65mm); Alt: (mu (does not equal sign) 1.65 mm) Average diameter is 1.65 mm, but we decide that it is not 1.65 mm. Average diameter is not 1.65 mm, but we don't find strong evidence that it is different than 1.65 mm

Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need to have a diameter of 1.65 mm—too big and they would hurt the donor (even more than usual), too small and they would rupture the red blood cells, rendering the donated blood useless. Thus, the manufacturing process would have to be closely monitored to detect any significant departures from the desired diameter. During every shift, quality control personnel take a sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected.​ Define the parameter of interest in the context of this study and assign an appropriate symbol to it. State the appropriate null and alternative hypotheses using the symbol defined in (a). Describe what a Type I error would be in this study. Describe what a Type II error would be in this study.

Education level Employment Ethnicity

Consider all of the countries in the world as the observational units in a study and answer the following questions. Which of the following are categorical variables that could be recorded on these countries? education level population median age employment ethnicity income levels

Income levels median age population

Consider all of the countries in the world as the observational units in a study and answer the following questions. Which of the following are quantitative variables that could be recorded on these countries? ethnicity income levels median age college education population employment

residence situation of each student

Consider the following question: "Is the residence situation of a college student (on-campus, off-campus with parents, off-campus without parents) related to how much alcohol the student consumes in a typical week?" Which of the following would be a categorical, non-binary variable? alcohol consumption of each student type of college residence situation of each student type of alcohol consumed

alcohol consumption of each student

Consider the following question: "Is the residence situation of a college student (on-campus, off-campus with parents, off-campus without parents) related to how much alcohol the student consumes in a typical week?" Which of the following would be a quantitative variable? type of college alcohol consumption of each student residence situation of each student type of alcohol consumed

true true exam scores colors of paper binary

Consider the scenario: "An instructor wants to investigate whether the color of paper (blue or green) on which an exam is printed has an effect on students' exam scores.​" The observational units in this scenario are the students. The variables in this scenario are the exam scores for each student and the color of paper on which the student took the exam. The quantitative variable in this scenario is the The categorical variable in this scenario is the The categorical variable in this scenario can be classified as

is/ are do not

Consider the scenario: "Statistical evidence was used in the murder trial of Kristen Gilbert, a nurse who was accused of killing patients. More than 1,000 eight-hour shifts were analyzed. Was the proportion of shifts with a death substantially higher for the shifts that Gilbert worked?​" The categorical variables(s) ___________ binary because they ____________ have more than two possible outcomes.

True true

Consider the scenario: "Statistical evidence was used in the murder trial of Kristen Gilbert, a nurse who was accused of killing patients. More than 1,000 eight-hour shifts were analyzed. Was the proportion of shifts with a death substantially higher for the shifts that Gilbert worked?​" The observational units in this scenario are the 8-hour shifts. The variables in this scenario are whether or not there was at least one death on a shift and if Kristin Gilbert had worked the shift.

True True Quantitative variable

Consider the scenario: "Subjects listened to 10 seconds of the Jackson 5's song "ABC" and then were asked how long they thought the song snippet lasted. Do people tend to overestimate the song length? In this scenario, the subjects are the observational units. In this scenario, how long the subjects thought the song snippet lasted is the variable. The length of the song represents a__________

Type I Error

Dogs have been domesticated for about 14,000 years. In that time, have they been able to develop an understanding of human gestures such as pointing or glancing? How about similar nonhuman cues? Researchers Udell, Giglio, and Wynne tested a small number of dogs in order to answer these questions. The researchers positioned the dogs about 2.5 meters from the experimenter. On each side of the experimenter were two cups. The experimenter would perform some sort of gesture (pointing, bowing, looking) toward one of the cups or there would be some other nonhuman gesture (a mechanical arm pointing, a doll pointing, or a stuffed animal looking) toward one of the cups. The researchers would then see whether the dog would go to the cup that was indicated. There were six dogs tested.We will look at one of the dogs in two of his sets of trials. This dog, a four-year-old mixed breed, was named Harley. Each trial involved one gesture and one pair of cups, with a total of 10 trials in a set. After investigating whether Harley the dog could select the correct cup more than 50% of the time in the long run, we found that the observed data provided very strong evidence that Harley the dog was doing better than random chance. Which type of error (I or II) could we possibly be making with this conclusion?

Harley is guessing, but we determine that he is not guessing Harley is not guessing, but we do not determine that he is not guessing

Dogs have been domesticated for about 14,000 years. In that time, have they been able to develop an understanding of human gestures such as pointing or glancing? How about similar nonhuman cues? Researchers Udell, Giglio, and Wynne tested a small number of dogs in order to answer these questions. The researchers positioned the dogs about 2.5 meters from the experimenter. On each side of the experimenter were two cups. The experimenter would perform some sort of gesture (pointing, bowing, looking) toward one of the cups or there would be some other nonhuman gesture (a mechanical arm pointing, a doll pointing, or a stuffed animal looking) toward one of the cups. The researchers would then see whether the dog would go to the cup that was indicated. There were six dogs tested.We will look at one of the dogs in two of his sets of trials. This dog, a four-year-old mixed breed, was named Harley. Each trial involved one gesture and one pair of cups, with a total of 10 trials in a set.You want to investigate whether Harley the dog could select the correct cup more than 50% of the time in the long run. Describe what a Type I error would be in this study. Describe what a Type II error would be in this study.

-3.47 (100 out of 400; 25%), -3.80 (20 out of 120; 16.7%), -4.17 (65 out of 300; 21.7%)

Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock, which explored players' choices in the game rock-paper-scissors.Suppose that you play the game with three different friends separately with the following results: Friend A chose scissors 100 times out of 400 games, Friend B chose scissors 20 times out of 120 games, and Friend C chose scissors 65 times out of 300 games. Suppose that for each friend you want to test whether the long-run proportion that the friend will pick scissors is less than 1/3.​ Select the appropriate standardized statistics for each friend from the null distribution produced by applet. -3.80 (100 out of 400; 25%), -3.47 (20 out of 120; 16.7%), -4.17 (65 out of 300; 21.7%) -4.17 (100 out of 400; 25%), -3.80 (20 out of 120; 16.7%), -3.47 (65 out of 300; 21.7%) -3.47 (100 out of 400; 25%), -4.17 (20 out of 120; 16.7%), -3.80 (65 out of 300; 21.7%) -3.47 (100 out of 400; 25%), -3.80 (20 out of 120; 16.7%), -4.17 (65 out of 300; 21.7%)

65/ 300 100/ 400

Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock, which explored players' choices in the game rock-paper-scissors.Suppose that you play the game with three different friends separately with the following results: Friend A chose scissors 100 times out of 400 games, Friend B chose scissors 20 times out of 120 games, and Friend C chose scissors 65 times out of 300 games. Suppose that for each friend you want to test whether the long-run proportion that the friend will pick scissors is less than 1/3.​ Select the strongest and least strong evidence of the long-run proportion that the friend will choose scissors is less than 1/3. The strongest evidence is The least strong evidence is

Friend D because this is more evidence against the null hypothesis

Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock, which explored players' choices in the game rock-paper-scissors.​​Suppose that you play the game with two other friends separately with the following results: Friend D chose rock 200 times out of 400 games, Friend E chose rock 20 times out of 40 games. Suppose that for each friend you want to test whether the long-run proportion that the friend will pick rock is more than 1/3. When both of the friends played rock the same proportion of times and one of their data provided more evidence against the null hypothesis, which friend's data yielded a larger standardized statistic? Friend D because this is more evidence against the null hypothesis Friend D because this is less evidence against the null hypothesis Friend E because this is more evidence against the null hypothesis Friend E because this is less evidence against the null hypothesis

Friend D because this is more evidence against the null hypothesis

Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock, which explored players' choices in the game rock-paper-scissors.​​Suppose that you play the game with two other friends separately with the following results: Friend D chose rock 200 times out of 400 games, Friend E chose rock 20 times out of 40 games. Suppose that for each friend you want to test whether the long-run proportion that the friend will pick rock is more than 1/3. When both of the friends played rock the same proportion of times and one of their data provided more evidence against the null hypothesis, which friend's data yielded a smaller p-value? Friend D because this is less evidence against the null hypothesis Friend E because this is more evidence against the null hypothesis Friend D because this is more evidence against the null hypothesis Friend E because this is less evidence against the null hypothesis

Friend D because a smaller standard deviation leads to a larger standardized statistic

Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock, which explored players' choices in the game rock-paper-scissors.​​Suppose that you play the game with two other friends separately with the following results: Friend D chose rock 200 times out of 400 games, Friend E chose rock 20 times out of 40 games. Suppose that for each friend you want to test whether the long-run proportion that the friend will pick rock is more than 1/3. When both of the friends played rock the same proportion of times and one of their data provided more evidence against the null hypothesis, which friend's null distribution had a smaller standard deviation? Friend D because a smaller standard deviation leads to a smaller standardized statistic Friend D because a smaller standard deviation leads to a larger standardized statistic Friend E because a larger standard deviation leads to a smaller standardized statistic Friend E because a larger standard deviation leads to a larger standardized statistic

Friend D because they played more games

Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock, which explored players' choices in the game rock-paper-scissors.​​Suppose that you play the game with two other friends separately with the following results: Friend D chose rock 200 times out of 400 games, Friend E chose rock 20 times out of 40 games. Suppose that for each friend you want to test whether the long-run proportion that the friend will pick rock is more than 1/3. Which friend's data do you think provides more evidence against the null hypothesis as both of the friends played rock the same proportion of times? Friend E because they played less games Friend D because they played more games Friend E because they played more games Friend D because they played less games

We have very strong evidence that the long-run proportion of times that a player starts with scissors is different from 33%.

Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock. We investigated some results of the game rock-paper-scissors, where the researchers had 119 people play rock-paper-scissors against a computer. They found 66 players (55.5%) started with rock, 39 (32.8%) started with paper, and 14 (11.8%) started with scissors. We want to see if players start with scissors with a long-term probability that is different from 1/3.​ Summarize the conclusion from the p-value. We have very strong evidence that the long-run proportion of times that a player starts with scissors is different from 33%. We have weak evidence that the long-run proportion of times that a player starts with scissors is different from 33%. We have strong evidence that the long-run proportion of times that a player starts with scissors is 33%. We have no evidence that the long-run proportion of times that a player starts with scissors is different from 33%.

0.00

Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock. We investigated some results of the game rock-paper-scissors, where the researchers had 119 people play rock-paper-scissors against a computer. They found 66 players (55.5%) started with rock, 39 (32.8%) started with paper, and 14 (11.8%) started with scissors. We want to see if players start with scissors with a long-term probability that is different from 1/3.​ Using an appropriate applet, find the p-value using a theory-based test (one-proportion z-test; normal approximation).(Round your answer to 2 decimal places, e.g. 0.58.)p-value =

Null: The long-run proportion of times that a player starts with scissors is 33%, π = 33%Alt: The long-run proportion of times that a player starts with scissors is different from 33%, π ≠ 33%

Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock. We investigated some results of the game rock-paper-scissors, where the researchers had 119 people play rock-paper-scissors against a computer. They found 66 players (55.5%) started with rock, 39 (32.8%) started with paper, and 14 (11.8%) started with scissors. We want to see if players start with scissors with a long-term probability that is different from 1/3.​ Which of the following states the appropriate null and alternative hypotheses in the context of this study, first in words and then in symbols? Null: The long-run proportion of times that a player starts with scissors is 50%, π = 50%Alt: The long-run proportion of times that a player starts with scissors is different from 50%, π ≠ 50% Null: The long-run proportion of times that a player starts with scissors is 33%, π = 33%Alt: The long-run proportion of times that a player starts with scissors is different from 33%, π ≠ 33% Null: The long-run proportion of times that a player starts with scissors is 33%, π = 33%Alt: The long-run proportion of times that a player starts with scissors is less than 33%, π < 33% Null: The long-run proportion of times that a player starts with scissors is 33%, π = 33%Alt: The long-run proportion of times that a player starts with scissors is more than 33%, π > 33%

parameter

If Dwyane Wade of the Miami Heat hits 52 out of his first 100 field goals in the 2013/2014 season, let's see how we might investigate if he is more likely than not to make a field goal. Based on these first 100 field goals, we want to find out what Dwyane's long-run proportion of making a field goal is. What statistical term refers to this proportion? parameter chance model sample size statistic

statistic

If Dwyane Wade of the Miami Heat hits 52 out of his first 100 field goals in the 2013/2014 season, let's see how we might investigate if he is more likely than not to make a field goal. What statistical term is given to the value 52 out of 100? chance model sample size statistic parameter

A: p-value= 0.395, B: p-value=0.007, C: p-value=0.961, D: p-value=0.174

In a race for U.S. president, is the taller candidate more likely to win? In the first election of the 20th century, Theodore Roosevelt (178 cm) defeated Alton B. Parker (175 cm). There have been 27 additional elections since then, for a total of 28. Of these, 25 elections had only two major party candidates with one taller than the other. In 19 of the 25 elections, the taller candidate won. In this exercise, we eliminate elections with more than two major party candidates as well as elections with two candidates of the same height. In addition, we eliminate the two elections in which George Washington was unopposed and five elections with missing data. Consider four different data sets:A. Elections from 1960 (Kennedy) to the present: n=14, p^=8/14=0.5714.B. Elections from Theodore Roosevelt (1904) to the present: n=25, p^=19/25=0.76C. Elections from John Adams (1796) through William McKinley (1900): n=16, p^=5/16=0.3125.D. Elections from John Adams (1796) to the present: n=41, p^=24/41=0.5854.​ The four p-values, from smallest to largest, are 0.007, 0.174, 0.395, 0.961. Match each data set (A-D) with its p-value. A: p-value=0.961, B: p-value=0.007, C: p-value=0.395, D: p-value=0.174 A: p-value= 0.395, B: p-value=0.007, C: p-value=0.961, D: p-value=0.174 A: p-value= 0.395, B: p-value=0.961, C: p-value=0.007, D: p-value=0.174 A: p-value= 0.007, B: p-value=0.395, C: p-value=0.961, D: p-value=0.174

Looking at the set of p-values suggests there is little evidence that taller candidates are more likely to win. In particular, looking at all presidential elections since 1796 yields a p-value of 0.174. Looking at an arbitrary subset of presidential elections (previous exercise) suggested a potentially significant result, but looking at more data suggested otherwise.

In a race for U.S. president, is the taller candidate more likely to win? In the first election of the 20th century, Theodore Roosevelt (178 cm) defeated Alton B. Parker (175 cm). There have been 27 additional elections since then, for a total of 28. Of these, 25 elections had only two major party candidates with one taller than the other. In 19 of the 25 elections, the taller candidate won. In this exercise, we eliminate elections with more than two major party candidates as well as elections with two candidates of the same height. In addition, we eliminate the two elections in which George Washington was unopposed and five elections with missing data. Consider four different data sets:A. Elections from 1960 (Kennedy) to the present: n=14, p^=8/14=0.5714.B. Elections from Theodore Roosevelt (1904) to the present: n=25, p^=19/25=0.76C. Elections from John Adams (1796) through William McKinley (1900): n=16, p^=5/16=0.3125.D. Elections from John Adams (1796) to the present: n=41, p^=24/41=0.5854.​ What do you conclude about the hypothesis that taller candidates are more likely to win? Looking at the set of p-values suggests there is little evidence that taller candidates are more likely to win. In particular, looking at all presidential elections since 1796 yields a p-value of 0.174. Looking at an arbitrary subset of presidential elections (previous exercise) suggested a potentially significant result, but looking at more data suggested otherwise. Looking at the set of p-values suggests there is evidence that taller candidates are less likely to win. Looking at the set of p-values suggests there is no evidence that taller candidates are more likely to win. Looking at the set of p-values suggests there no evidence that taller candidates are more likely to win. In particular, looking at all presidential elections since 1796 yields a p-value of 0.961. Looking at an arbitrary subset of presidential elections (previous exercise) suggested a potentially significant result, but looking at more data suggested otherwise.

Yes, it is somewhat arbitrary to only look at 20th century elections.

In a race for U.S. president, is the taller candidate more likely to win?In the first election of the 20th century, Theodore Roosevelt (178 cm) defeated Alton B. Parker (175 cm). There have been 27 additional elections since then, for a total of 28. Of these, 25 elections had only two major party candidates with one taller than the other. In 19 of the 25 elections, the taller candidate won. Are there reasons not to take the p-value at face value? If yes, list them. Yes, the sample size is too small. Yes, it is somewhat arbitrary to only look at 20th century elections. Yes, the sample size is too large. No, there are no reasons not to take p-value at face value.

We have very strong evidence against the null and in support of the taller candidate winning the race more often than would be predicted by random chance.

In a race for U.S. president, is the taller candidate more likely to win?In the first election of the 20th century, Theodore Roosevelt (178 cm) defeated Alton B. Parker (175 cm). There have been 27 additional elections since then, for a total of 28. Of these, 25 elections had only two major party candidates with one taller than the other. In 19 of the 25 elections, the taller candidate won. If you take the p-value at face value, what do you conclude? We have very strong evidence against the null and in support of the taller candidate winning the race more often than would be predicted by random chance. We have very weak evidence against the null and in support of the taller candidate winning the race more often than would be predicted by random chance. We have very strong evidence against the null and in support of the taller candidate not winning the race more often than would be predicted by random chance. We have very weak evidence against the null and in support of the taller candidate not winning the race more often than would be predicted by random chance.

In a race for U.S. president, is the taller candidate more likely to win? Alternatively, is π > 0.5?

In a race for U.S. president, is the taller candidate more likely to win?In the first election of the 20th century, Theodore Roosevelt (178 cm) defeated Alton B. Parker (175 cm). There have been 27 additional elections since then, for a total of 28. Of these, 25 elections had only two major party candidates with one taller than the other. In 19 of the 25 elections, the taller candidate won. Let π = P (taller wins). State the research hypothesis in words and in symbols. In a race for U.S. president, is the taller candidate less likely to win? Alternatively, is π < 0.5? In a race for U.S. president, is the taller candidate less likely to win? Alternatively, is π > 0.5? In a race for U.S. president, is the taller candidate more likely to win? Alternatively, is π > 0.5? In a race for U.S. president, is the taller candidate more likely to win? Alternatively, is π < 0.5?

Null: The long-run proportion of races where the taller candidate wins in U.S. presidential elections is 0.5;Alt: The long-run proportion of races where the taller candidate wins in U.S. presidential elections is larger than 0.5.​Using symbols: H0: π = 0.5, Ha: π > 0.5; where π is the long-run proportion of races where the taller candidate won.

In a race for U.S. president, is the taller candidate more likely to win?In the first election of the 20th century, Theodore Roosevelt (178 cm) defeated Alton B. Parker (175 cm). There have been 27 additional elections since then, for a total of 28. Of these, 25 elections had only two major party candidates with one taller than the other. In 19 of the 25 elections, the taller candidate won. State the null and alternative hypotheses in words and symbols. Null: The long-run proportion of races where the taller candidate wins in U.S. presidential elections is 0.7;Alt: The long-run proportion of races where the taller candidate wins in U.S. presidential elections is smaller than 0.4.​Using symbols: H0: π = 0.7, Ha: π < 0.4; where π is the long-run proportion of races where the taller candidate won. Null: The long-run proportion of races where the taller candidate wins in U.S. presidential election is 0.8;Alt: The long-run proportion of races where the taller candidate wins in U.S. presidential elections is smaller than 0.6.​​Using symbols: H0: π = 0.8, Ha: π < 0.6; where π is the long-run proportion of races where the taller candidate won. Null: The long-run proportion of races where the taller candidate wins in U.S. presidential elections is 0.7;Alt: The long-run proportion of races where the taller candidate wins in U.S. presidential elections is smaller than 0.5.​Using symbols: H0: π = 0.7, Ha: π < 0.5; where π is the long-run proportion of races where the taller candidate won. Null: The long-run proportion of races where the taller candidate wins in U.S. presidential elections is 0.5;Alt: The long-run proportion of races where the taller candidate wins in U.S. presidential elections is larger than 0.5.​Using symbols: H0: π = 0.5, Ha: π > 0.5; where π is the long-run proportion of races where the taller candidate won.

probability of heads: 0.5, number of tosses: 25, approximate p-value = 0.0071

In a race for U.S. president, is the taller candidate more likely to win?In the first election of the 20th century, Theodore Roosevelt (178 cm) defeated Alton B. Parker (175 cm). There have been 27 additional elections since then, for a total of 28. Of these, 25 elections had only two major party candidates with one taller than the other. In 19 of the 25 elections, the taller candidate won. What is the p-value of this test? probability of heads: 0.5, number of tosses: 25, approximate p-value = 0.0071 probability of heads: 0.25, number of tosses: 25, approximate p-value = 0.0071 probability of heads: 0.25, number of tosses: 25, approximate p-value = 0.0007 probability of heads: 0.5, number of tosses: 25, approximate p-value = 0.0007

parameter, statistic

In most statistical studies the ________ is unknown and the __________ is known

The proportion of U.S. adults who are unhappy with the verdict.

In order to understand more about how people in the U.S. feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers go to the news program's website and indicate their opinion about the event. At the end of the show 80% of the people who voted in the poll indicated they were unhappy with the verdict.​ Describe in words the parameter of interest. The proportion of U.S. adults who are unhappy with the verdict. The proportion of U.S. adults who are happy with the verdict. The proportion of U.S. adults that are not viewers of the television program. The proportion of U.S. adults that are viewers of the television program.

0.8

In order to understand more about how people in the U.S. feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers go to the news program's website and indicate their opinion about the event. At the end of the show 80% of the people who voted in the poll indicated they were unhappy with the verdict.​ Identify the numeric value of the statistic corresponding to the above parameter, as found in the television news survey.

Theory-based is appropriate because there are at least 10 successes and 10 failures in the data, p = 0.0001.

In order to understand more about how people in the U.S. feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers go to the news program's website and indicate their opinion about the event. At the end of the show 82% of the 562 people who voted in the poll indicated they were unhappy with the verdict.​ Evaluate the strength of evidence for the hypothesis that the proportion of U.S. adults opposed to the verdict is greater than 0.75. Explain why a theory-based approach is or is not reasonable for these data. If a theory-based approach is reasonable, find the p-value. Theory-based is not appropriate because there are not enough data values. Theory-based is appropriate because there are at least 10 successes and 10 failures in the data, p = 0.0002. Theory-based is appropriate because there are at least 10 successes and 10 failures in the data, p = 0.0001. Theory-based is appropriate because there are at least 10 successes and 10 failures in the data, p = 0.1.

There is strong evidence that the proportion of U.S. adults opposed to the verdict is greater than 7 Comfortable in generalizing to all people who watch this program and are motivated to participate

In order to understand more about how people in the U.S. feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers go to the news program's website and indicate their opinion about the event. At the end of the show 82% of the 562 people who voted in the poll indicated they were unhappy with the verdict.​ Evaluate the strength of evidence for the hypothesis that the proportion of U.S. adults opposed to the verdict is greater than 0.75. Find the p-value for the hypothesis using a simulation-based approach. Based on the p-value evaluate the strength of evidence and state a conclusion about the opinions of U.S. adults about the verdict. To which population, if any, are you comfortable drawing your conclusion?

bar graph

In order to understand more about how people in the U.S. feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers go to the news program's website and indicate their opinion about the event. At the end of the show 82% of the people who voted in the poll indicated they were unhappy with the verdict.​ Identify one graph that the news program could use to summarize the variable. Bar graph Line graph Histogram Scatter plot

Proportion

In order to understand more about how people in the U.S. feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers go to the news program's website and indicate their opinion about the event. At the end of the show 82% of the people who voted in the poll indicated they were unhappy with the verdict.​ Identify one statistic that the news program could use to summarize the variable. Median Mode Proportion Mean

Whether someone is unhappy with the verdict categorical

In order to understand more about how people in the U.S. feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers go to the news program's website and indicate their opinion about the event. At the end of the show 82% of the people who voted in the poll indicated they were unhappy with the verdict.​ Identify the variable measured on each participant in the survey. Is the variable categorical or quantitative?

The population is all adults in the United States It is perhaps greater than the population proportion because the people who voluntarily went to the ...

In order to understand more about how people in the U.S. feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers go to the news program's website and indicate their opinion about the event. At the end of the show 82% of the people who voted in the poll indicated they were unhappy with the verdict.​ What is the population of interest? Do you believe that the proportion of people unhappy with the verdict in the sample is likely less than, similar to, or greater than the proportion of individuals unhappy with the verdict in the population?

0.66

In order to understand more about how people in the U.S. feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers go to the news program's website and indicate their opinion about the event. At the end of the show 82% of the people who voted in the poll indicated they were unhappy with the verdict.​ The news program wishes to test whether there is evidence that more than three-quarters of U.S. adults are unhappy with the verdict. Five hundred and sixty-two participants participated in the survey, of which 66% said that they were unhappy with the verdict. What is the value of the statistic? Give your answer as a proportion.

Null: The proportion of voters who are unhappy is 0.75 Alternative: The proportion of voters who are unhappy is greater than 0.75

In order to understand more about how people in the U.S. feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers go to the news program's website and indicate their opinion about the event. At the end of the show 82% of the people who voted in the poll indicated they were unhappy with the verdict.​ The news program wishes to test whether there is evidence that more than three-quarters of U.S. adults are unhappy with the verdict. Five hundred and sixty-two participants participated in the survey, of which 82% said that they were unhappy with the verdict. State the null and alternative hypotheses for this test. Null: Alternative:

reject

Indicate whether or not you would reject the null hypothesis, at the α = 0.05 significance level, for the p-value = 0.001.

Reject

Indicate whether or not you would reject the null hypothesis, at the α = 0.05 significance level, for the p-value = 0.045.

fail to reject

Indicate whether or not you would reject the null hypothesis, at the α = 0.05 significance level, for the p-value = 0.051.

Fail to reject

Indicate whether or not you would reject the null hypothesis, at the α = 0.05 significance level, for the p-value = 0.078.

fail to reject

Indicate whether or not you would reject the null hypothesis, with a p-value of 0.064, for the significance level α = 0.01.

fail to reject

Indicate whether or not you would reject the null hypothesis, with a p-value of 0.064, for the significance level α = 0.05.

reject

Indicate whether or not you would reject the null hypothesis, with a p-value of 0.064, for the significance level α = 0.065.

reject

Indicate whether or not you would reject the null hypothesis, with a p-value of 0.064, for the significance level α = 0.10.

college students

Is the residence situation of a college student (on-campus, off -campus with parents, off -campus without parents) related to how much alcohol the student consumes in a typical week? Answer each of the following questions. Identify the observational units in this question: "Is the residence situation of a college student (on-campus, off-campus with parents, off-campus without parents) related to how much alcohol the student consumes in a typical week?" volume of alcohol consumed college students place of residence where alcohol is consumed

alcohol consumption of each student and residence situation of each student

Is the residence situation of a college student (on-campus, off -campus with parents, off -campus without parents) related to how much alcohol the student consumes in a typical week? Answer each of the following questions. Identify the variables in this question: "Is the residence situation of a college student (on-campus, off-campus with parents, off-campus without parents) related to how much alcohol the student consumes in a typical week?" alcohol consumption of each student and types of alcohol consumed alcohol consumption of each student and residence situation of each student age of student and residence situation of each student type of alcohol consumed and age of student

True

Larger random samples are always better than smaller random samples. True False

False

Larger samples are always better than smaller samples, regardless of how the sample was collected. True False

Flip a coin 1354 times and record the number of heads. Repeat this 1000 times, keeping track of the number of heads in each set of 1354.

LeBron James of the Miami Heat hit 765 of his 1354 field goal attempts in the 2012/2013 season for a shooting percentage of 56.5%. Over the lifetime of LeBron's career, can we say he is more likely than not to make a field goal?​ Describe how to use coin flipping to simulate the 2012/2013 season under the assumption of the chance model. Flip a coin 1354 times and record the number of heads. This number represents the long-run proportion. Flip a coin 1000 times and record the number of heads. Repeat this process 765 times. Flip a coin 1354 times and record the number of heads. Repeat this 1000 times, keeping track of the number of heads in each set of 1354. Flip a coin 765 times and record the number of heads. Multiply this value by 1354.

LeBron's long-run proportion of making a field goal

LeBron James of the Miami Heat hit 765 of his 1354 field goal attempts in the 2012/2013 season for a shooting percentage of 56.5%. Over the lifetime of LeBron's career, can we say he is more likely than not to make a field goal?​ Describe the parameter of interest. LeBron's long-run proportion of making a field goal the proportion of all shots made by NBA players in LeBron's career the number of shots LeBron made in the 2012/2013 season the proportion of shots LeBron made in the 2012/2013 season

Approximately ½ of 1354 (677) will be one of the most likely values since we assume the chance model is true.

LeBron James of the Miami Heat hit 765 of his 1354 field goal attempts in the 2012/2013 season for a shooting percentage of 56.5%. Over the lifetime of LeBron's career, can we say he is more likely than not to make a field goal?​ Suppose coin flipping was used to simulate the 2012/2013 season under the assumption of the chance model. What would be a typical number of heads recorded from a repetition of 1354 coin flips? Nothing can be known about the typical number of heads without doing the simulation. Approximately ½ of 1354 (677) will be one of the most likely values since we assume the chance model is true. 56.5% of 1354 (765) will be one of the most likely values since we assume the chance model is true and the chance probability is 56.5%. LeBron James is a great player so we can assume he will make at least 60% of his shots.

statistic

LeBron James of the Miami Heat hit 765 of his 1354 field goal attempts in the 2012/2013 season for a shooting percentage of 56.5%. Over the lifetime of LeBron's career, can we say he is more likely than not to make a field goal?​ What statistical term is given to the value 56.5%? chance model sample parameter statistic

50%

LeBron James of the Miami Heat hit 765 of his 1354 field goal attempts in the 2012/2013 season for a shooting percentage of 56.5%. Over the lifetime of LeBron's career, can we say he is more likely than not to make a field goal?​ What value would the chance model assign to LeBron's long-run proportion of making a field goal? 50% 765 25% 56.5%

28/40 = 0.7 is the sample proportion; the symbol p-hat denotes this quantity.

Love, firstA recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. One aspect of the study involved 47 heterosexual couples who are part of an online pool of people willing to participate in surveys. These 47 couples were asked about which person was the first to say "I love you." For 7 of those couples, the two people disagreed about the answer to this question. But both people agreed for the other 40 couples, so those 40 responses were included in the analysis. Previous studies have suggested that males tend to say "I love you" first.​​ It turned out that for 28 of the 40 couples in the sample (after the 7 couples who could not agree were excluded), the man said "I love you" before the woman did.​​What is the sample proportion of couples for whom the man was the first to say "I love you"? What symbol is used to denote this statistic? 28/40 = 0.7 is the sample proportion; the symbol H0 denotes this quantity. 28/40 = 0.7 is the sample proportion; the symbol p-hat denotes this quantity. 28/40 = 0.7 is the sample proportion; the symbol Ha denotes this quantity. 28/40 = 0.7 is the sample proportion; the symbol π denotes this quantity.

The p-value is the probability of observing a value of 28 or greater, assuming that for 50% of couples the man said "I love you" first.

Love, firstA recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. One aspect of the study involved 47 heterosexual couples who are part of an online pool of people willing to participate in surveys. These 47 couples were asked about which person was the first to say "I love you." For 7 of those couples, the two people disagreed about the answer to this question. But both people agreed for the other 40 couples, so those 40 responses were included in the analysis. Previous studies have suggested that males tend to say "I love you" first.​​ Select the interpretation of this p-value with the probability and hypothesis assumption. The p-value is the probability of observing a value of 28 or greater, assuming that for less than 50% of couples the man said "I love you" first. The p-value is the probability of observing a value of 28 or less, assuming that for 50% of couples the man said "I love you" first. The p-value is the probability of observing a value of 28 or greater, assuming that for more than 50% of couples the man said "I love you" first. The p-value is the probability of observing a value of 28 or greater, assuming that for 50% of couples the man said "I love you" first.

categorical

Love, firstA recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. One aspect of the study involved 47 heterosexual couples who are part of an online pool of people willing to participate in surveys. These 47 couples were asked about which person was the first to say "I love you." For 7 of those couples, the two people disagreed about the answer to this question. But both people agreed for the other 40 couples, so those 40 responses were included in the analysis. Previous studies have suggested that males tend to say "I love you" first.​​ The 40 heterosexual couples who agreed on their response to which person was the first to say "I love you" are the observational units. Whether the man or woman said "I love you" first is a Choose the answer from the menu in accordance to the question statement ___________ variable

couples

Love, firstA recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. One aspect of the study involved 47 heterosexual couples who are part of an online pool of people willing to participate in surveys. These 47 couples were asked about which person was the first to say "I love you." For 7 of those couples, the two people disagreed about the answer to this question. But both people agreed for the other 40 couples, so those 40 responses were included in the analysis. Previous studies have suggested that males tend to say "I love you" first.​​ The symbol π in this context stands for the long-term proportion of all________ where the man said "I love you" first

0.008

Love, firstA recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. One aspect of the study involved 47 heterosexual couples who are part of an online pool of people willing to participate in surveys. These 47 couples were asked about which person was the first to say "I love you." For 7 of those couples, the two people disagreed about the answer to this question. But both people agreed for the other 40 couples, so those 40 responses were included in the analysis. Previous studies have suggested that males tend to say "I love you" first.​​ Use an applet to conduct a simulation with π = 0.5, n = 40, and number of repetitions = 1000. We find the proportion of times a value greater than or equal to 28 is observed. The p-value is approximately

Flip a coin 40 times and keep track of the number of heads. Repeat the 40 coin flips 1000 times. Calculate the proportion of sets of 40 coin flips where 28 or more heads were obtained. That proportion is the p-value.

Love, firstA recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. One aspect of the study involved 47 heterosexual couples who are part of an online pool of people willing to participate in surveys. These 47 couples were asked about which person was the first to say "I love you." For 7 of those couples, the two people disagreed about the answer to this question. But both people agreed for the other 40 couples, so those 40 responses were included in the analysis. Previous studies have suggested that males tend to say "I love you" first.​​ Which of the following best describes how you could use a coin-flipping model to determine the p-value for this situation? Flip a coin 40 times and keep track of the number of heads. Repeat the 40 coin flips 1000 times. Calculate the proportion of sets of 40 coin flips where exactly 28 heads were obtained. That proportion is the p-value. Flip a coin 40 times and keep track of the number of heads. Repeat the 40 coin flips 100 times. Calculate the proportion of sets of 40 coin flips where 28 or more heads were obtained. That proportion is the p-value. Flip a coin 40 times and keep track of the number of heads. Repeat the 40 coin flips 10 times. Calculate the proportion of sets of 40 coin flips where 8 or more heads were obtained. That proportion is the p-value. Flip a coin 40 times and keep track of the number of heads. Repeat the 40 coin flips 1000 times. Calculate the proportion of sets of 40 coin flips where 28 or more heads were obtained. That proportion is the p-value.

Null: The proportion of all couples where the male said "I love you" first is 0.50.Alt: The proportion of all couples where the male said "I love you" first is greater than 0.50

Love, firstA recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. One aspect of the study involved 47 heterosexual couples who are part of an online pool of people willing to participate in surveys. These 47 couples were asked about which person was the first to say "I love you." For 7 of those couples, the two people disagreed about the answer to this question. But both people agreed for the other 40 couples, so those 40 responses were included in the analysis. Previous studies have suggested that males tend to say "I love you" first.​​ Which of the following describes the best null and alternative hypotheses regarding if males are more likely to say "I love you" first? Null: The proportion of all couples where the female said "I love you" first is 0.50.Alt: The proportion of all couples where the female said "I love you" first is greater than 0.50 Null: The proportion of all couples where the male said "I love you" first is 0.50.Alt: The proportion of all couples where the male said "I love you" first is less than 0.50 Null: The proportion of all couples where the male said "I love you" first is 0.50.Alt: The proportion of all couples where the male said "I love you" first is greater than 0.50 Null: The proportion of all couples where the female said "I love you" first is 0.50.Alt: The proportion of all couples where the male said "I love you" first is less than 0.50

1.51

Most people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist Onur Güntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks.They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 127 couples, age 13-70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.The null hypothesis in the original study was H0: π = 0.50; suppose our null hypothesis was H0: π = 0.60. In the context of this null hypothesis, determine the standardized statistic from the data where 84 of 127 kissing couples leaned their heads right.​Hint: You will need to get the standard deviation of the simulated statistics from the null distribution.​(Round your answer to 2 decimal places, e.g. 52.75.)

The observed proportion of couples who leaned to the right when kissing is 1.5standard deviations above the null hypothesized value of 0.60.

Most people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist Onur Güntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks.They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 127 couples, age 13-70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.The null hypothesis in the original study was H0: π = 0.50; suppose our null hypothesis was H0: π = 0.60. Interpret the meaning of the standardized statistic. The observed proportion of couples who leaned to the right when kissing is 1.5standard deviations above the null hypothesized value of 0.60. The observed proportion of couples who leaned to the right when kissing is 1.5standard deviations below the null hypothesized value of 0.60. The observed proportion of couples who leaned to the right when kissing is 1.5standard deviations away from the null hypothesized value of 0.60.

The standardized statistic is smaller. This makes sense because the null hypothesis is now closer to the observed statistic (less extreme).

Most people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist Onur Güntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks.They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 127 couples, age 13-70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.The null hypothesis in the original study was H0: π = 0.50; suppose our null hypothesis was H0: π = 0.60. Select the best comparison between this standardized statistic and the statistic based on a null hypothesis of π = 0.50. The standardized statistic is larger. This makes sense because the null hypothesis is not closer to the observed statistic (less extreme). The standardized statistic is smaller. This makes sense because the null hypothesis is now closer to the observed statistic (less extreme). The standardized statistic is smaller. This makes sense because the null hypothesis is not closer to the observed statistic (less extreme). The standardized statistic is larger. This makes sense because the null hypothesis is now closer to the observed statistic (less extreme).

The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations above the null hypothesized value of 0.50.

Most people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist OnurGüntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 124 couples, ages 13-70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.​ Interpret the meaning of the standardized statistic. The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations above the null hypothesized value of 0.50. The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations away from the null hypothesized value of 0.50. The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations below the null hypothesized value of 0.50.

0.645 3.22

Most people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist OnurGüntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 124 couples, ages 13-70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.​ Of the 124 kissing couples, 80 were observed to lean their heads right. What is the observed proportion of kissing couples who leaned their heads to the right? What symbol should you use to represent this value? (Round answer to 3 decimal places, e.g. 5.275) Determine the standardized statistic from the data. ​(Hint: You will need to get the standard deviation of the simulated statistics from the null distribution.) (Round answer to 2 decimal places, e.g. 52.75)

We have strong evidence that the proportion of couples that lean their heads to the right while kissing is more than 50%.

Most people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist OnurGüntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 124 couples, ages 13-70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.​ Select the best conclusion that you would draw about the null and alternate hypotheses. We have strong evidence that the proportion of couples that lean their heads to the right while kissing is less than 50%. We have strong evidence that the proportion of couples that lean their heads to the right while kissing is near to 50%. We have strong evidence that the proportion of couples that lean their heads to the right while kissing is 50%. We have strong evidence that the proportion of couples that lean their heads to the right while kissing is more than 50%.

right

Most people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist OnurGüntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 124 couples, ages 13-70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.​ The symbol π represents the long-run proportion of all the couples that lean their heads _________ while kissing

null: π = 0.5, alternative: π > 0.5

Most people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist OnurGüntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 124 couples, ages 13-70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.​ Which of the following best describes the null hypothesis and the alternative hypothesis using π? null: π = 0.5, alternative: π < 0.5 null: π ≠ 0.5, alternative: π > 0.5 null: π = 0.5, alternative: π > 0.5 null: π ≠ 0.5, alternative: π < 0.5

false

Nonrandom samples are always biased. True False

We have strong evidence that the long-run proportion of people who will pick the number 3 is greater than 25%

One of the authors read somewhere that it's been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.To investigate this, she collected data in her class. Here is the table of responses from her students: Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Based on the p-value, select the best conclusion that you would draw about the research question of whether when people are asked to choose from the numbers 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance. We have very strong evidence that the long-run proportion of people who will pick the number 3 is greater than 25% We have moderate evidence that the long-run proportion of people who will pick the number 3 is greater than 25% We have little to no evidence that the long-run proportion of people who will pick the number 3 is greater than 25% We have strong evidence that the long-run proportion of people who will pick the number 3 is greater than 25%

The p-value is small and the standardized statistic is large

One of the authors read somewhere that it's been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.To investigate this, she collected data in her class. Here is the table of responses from her students: Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Choose all that apply. The p-value is large and the standardized statistic is large The p-value is small and the standardized statistic is large The p-value is small and the standardized statistic is small The p-value is large and the standardized statistic is small

The p-value is approximately 0.02, and is the probability of 14 or more of the 33 people choosing "3", assuming that people do not tend to choose "3" more frequently than either of "1", "2" or "4".

One of the authors read somewhere that it's been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.To investigate this, she collected data in her class. Here is the table of responses from her students: Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Select the p-value from the options using appropriate applet, and interpret that p-value. The p-value is approximately 0.20, and is the probability of 14 or more of the 33 people choosing "3", assuming that people do not tend to choose "3" more frequently than either of "1", "2" or "4". The p-value is approximately 0.02, and is the probability of 14 or more of the 33 people choosing "3", assuming that people tend to choose "3" more frequently than either of "1", "2" or "4". The p-value is approximately 0.02, and is the probability of 14 or more of the 33 people choosing "3", assuming that people do not tend to choose "3" more frequently than either of "1", "2" or "4". The p-value is approximately 0.002, and is the probability of 14 or more of the 33 people choosing "3", assuming that people do not tend to choose "3" more frequently than either of "1", "2" or "4".

2.27

One of the authors read somewhere that it's been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.To investigate this, she collected data in her class. Here is the table of responses from her students: Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 The value of the standardized statistic is approximately

We have little to no evidence that the long-run proportion of people who will pick a big number 3 is greater than 50%

One of the authors read somewhere that it's been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.To investigate this, she collected data in her class. Here is the table of responses from her students: Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Suppose that you wanted to investigate whether people tend to pick a "big" number (3 or 4) rather than a "small" number (1 or 2).​​ Based on the p-value, select the best conclusion that you would draw about the research question "when people are asked to pick a number from the choices 1, 2, 3, and 4, they tend to pick a "big" number." We have very strong evidence that the long-run proportion of people who will pick a big number is greater than 50% We have little to no evidence that the long-run proportion of people who will pick a big number 3 is greater than 50% We have moderate evidence that the long-run proportion of people who will pick a big number is greater than 50% We have strong evidence that the long-run proportion of people who will pick a big number is greater than 50%

False

One of the authors read somewhere that it's been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.To investigate this, she collected data in her class. Here is the table of responses from her students: Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Suppose that you wanted to investigate whether people tend to pick a "big" number (3 or 4) rather than a "small" number (1 or 2).​​ Based on the value of the standardized statistic being approximately 0.87, the p-value will be small. True False

The p-value is large and the standardized statistic is small

One of the authors read somewhere that it's been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.To investigate this, she collected data in her class. Here is the table of responses from her students: Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Suppose that you wanted to investigate whether people tend to pick a "big" number (3 or 4) rather than a "small" number (1 or 2).​​ Choose all that apply. The p-value is small and the standardized statistic is small The p-value is small and the standardized statistic is large The p-value is large and the standardized statistic is small The p-value is large and the standardized statistic is large

We have little to no evidence that the long-run proportion of people who will pick a big number 3 is greater than 50%

One of the authors read somewhere that it's been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.To investigate this, she collected data in her class. Here is the table of responses from her students: Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Suppose that you wanted to investigate whether people tend to pick a "big" number (3 or 4) rather than a "small" number (1 or 2).​​ Select the best conclusion that you would draw about the research question of whether people tend to pick a "big" number. We have very strong evidence that the long-run proportion of people who will pick a big number is greater than 50% We have strong evidence that the long-run proportion of people who will pick a big number is greater than 50% We have moderate evidence that the long-run proportion of people who will pick a big number is greater than 50% We have little to no evidence that the long-run proportion of people who will pick a big number 3 is greater than 50%

The p-value is approximately 0.153, and is the probability 19 or more of the 33 people would choose a "big" number, assuming people do not tend to choose "big" numbers.

One of the authors read somewhere that it's been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.To investigate this, she collected data in her class. Here is the table of responses from her students: Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Suppose that you wanted to investigate whether people tend to pick a "big" number (3 or 4) rather than a "small" number (1 or 2).​​ Select the p-value from the options using an appropriate applet, and interpret that p-value. The p-value is approximately 0.153, and is the probability 19 or more of the 33 people would choose a "big" number, assuming people do not tend to choose "big" numbers. The p-value is approximately 0.153, and is the probability 19 or fewer of the 33 people would choose a "big" number, assuming people tend to choose "big" numbers. The p-value is approximately 0.153, and is the probability 19 or more of the 33 people would choose a "big" number, assuming people tend to choose "big" numbers. The p-value is approximately 0.153, and is the probability 19 or fewer of the 33 people would choose a "big" number, assuming people do not tend to choose "big" numbers.

0.50, 0.087 0.870

One of the authors read somewhere that it's been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.To investigate this, she collected data in her class. Here is the table of responses from her students: Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Suppose that you wanted to investigate whether people tend to pick a "big" number (3 or 4) rather than a "small" number (1 or 2).​​ Use an applet to generate the null distribution of the proportion of "successes." Report the mean and SD of this null distribution. (Round answer to 3 decimal places, e.g. 527.5) The mean is ________ and the SD is ________ Determine the standardized statistic for the observed sample proportion of "successes". (Round answer to 3 decimal places, e.g. 527.5)

null: π=0.5, alternative: π>0.5

One of the authors read somewhere that it's been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.To investigate this, she collected data in her class. Here is the table of responses from her students: Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Suppose that you wanted to investigate whether people tend to pick a "big" number (3 or 4) rather than a "small" number (1 or 2).​​ Which of the following best describes the null hypothesis and the alternative hypothesis using the appropriate symbol? null: π=0.5, alternative: π>0.5 null: p^=0.5, alternative: p^>0.5 null: p^=0.5, alternative: p^<0.5 null: π=0.5, alternative: π<0.5

If you repeatedly select an adult American at random a large number of times, in the long run, roughly 30% of the time the selected adult will vote to get rid of the penny.

Pennies can be a nuisance. Suppose 30% of the population of adult Americans want to get rid of the penny. If I randomly select one person from this population, the probability this person wants to get rid of the penny is 0.30. If you repeatedly select an adult American at random a large number of times, in the long run, roughly 30% of the time the selected adult will vote to get rid of the penny. If you ask 10 people if they are in favor of getting rid of the penny, 3 of them will say yes. There are 30 out of every 100 people who would agree that they would vote to get rid of the penny. All of these are correct.

False

Random samples only generate unbiased estimates of long-run proportions, NOT long-run means. True False

be weaker

Refer to example 1.1 in the text involving two dolphins, Buzz and Doris, where the researcher Dr. Bastian was investigating whether dolphins can communicate. Recall that Buzz pushed the correct lever 15 out of 16 times when given the choice between two levers to push. Suppose he had guessed right 14 times out of 16. Overall, the evidence against the null hypothesis would be stronger. be inadequate. have no change. be weaker.

distance

Refer to example 1.1 in the text involving two dolphins, Buzz and Doris, where the researcher Dr. Bastian was investigating whether dolphins can communicate. Recall that Buzz pushed the correct lever 15 out of 16 times when given the choice between two levers to push. Suppose he had guessed right 14 times out of 16. Which of the influences on strength of evidence would change? one- or two-sided sample size distance

be stronger

Refer to example 1.1 in the text involving two dolphins, Buzz and Doris, where the researcher Dr. Bastian was investigating whether dolphins can communicate. Recall that Buzz pushed the correct lever 15 out of 16 times when given the choice between two levers to push. Suppose the numbers had been exactly double that: 30 right out of 32.​ Overall, the evidence against the null hypothesis would have no changes. be inadequate. be weaker. be stronger.

sample size

Refer to example 1.1 in the text involving two dolphins, Buzz and Doris, where the researcher Dr. Bastian was investigating whether dolphins can communicate. Recall that Buzz pushed the correct lever 15 out of 16 times when given the choice between two levers to push. Suppose the numbers had been exactly double that: 30 right out of 32.​ Which of the influences on strength of evidence would change? distance sample size one- or two-sided

doubling it; the alternative would now be two-sided weaker

Refer to the example in the text involving two dolphins, Buzz and Doris, where the researcher Dr. Bastian was investigating whether dolphins can communicate. Recall that Buzz pushed the correct lever 15 out of 16 times when given the choice between two levers to push. Just for the sake of this exercise, imagine that the investigators wanted their statistical test to include the possibility that Buzz was a very sadistic dolphin, so malicious that he would willingly give up his own chance at a fish just to deprive Doris.​ This thinking would affect the p-value based on the actual data (15 right out of 16) by Suppose he had only guessed right 14 times out of 16. The reframing of the alternative hypothesis makes the evidence against the null hypothesis

moderately strong

Researchers wanted to test the hypothesis that living in the country is better for your lungs than living in a city. To eliminate the possible variation due to genetic differences, they located seven pairs of identical twins with one member of each twin living in the country, the other in a city. For each person, they measured the percentage of inhaled tracer particles remaining in the lungs after one hour: the higher the percentage, the less healthy the lungs. They found that for six of the seven twin pairs the one living in the country had healthier lungs.​ Based on the sample size and distance between the null value and the observed proportion, estimate the strength of evidence. weak but suggestive weak moderately strong inconclusive overwhelming

p-value = 0.0547 + 0.0078 = 0.0625 we have moderate evidence that individuals living in the country have healthier lungs than those of individuals living in cities.

Researchers wanted to test the hypothesis that living in the country is better for your lungs than living in a city. To eliminate the possible variation due to genetic differences, they located seven pairs of identical twins with one member of each twin living in the country, the other in a city. For each person, they measured the percentage of inhaled tracer particles remaining in the lungs after one hour: the higher the percentage, the less healthy the lungs. They found that for six of the seven twin pairs the one living in the country had healthier lungs.​ Here are probabilities for the number of heads in seven tosses of a fair coin: Heads: 0, 1, 2, 3, 4, 5, 6, 7 Probability:0.0078, 0.547, 0.1641, 0.2734, 0.2734, 0.1641, 0.547, 0.0078 Compute the p-value and state your conclusion.​​ p-value = 0.0547 + 0.0547 = 0.1094 we have moderate evidence that individuals living in the country have healthier lungs than those of individuals living in cities. p-value = 0.0547 we have moderate evidence that individuals living in the country have healthier lungs than those of individuals living in cities. p-value = 0.0547 + 0.0078 = 0.0625 we have moderate evidence that individuals living in the country have healthier lungs than those of individuals living in cities. p-value = 0.0078 + 0.0078 = 0.0156 we have moderate evidence that individuals living in the country have healthier lungs than those of individuals living in cities.

one-sided

Researchers wanted to test the hypothesis that living in the country is better for your lungs than living in a city. To eliminate the possible variation due to genetic differences, they located seven pairs of identical twins with one member of each twin living in the country, the other in a city. For each person, they measured the percentage of inhaled tracer particles remaining in the lungs after one hour: the higher the percentage, the less healthy the lungs. They found that for six of the seven twin pairs the one living in the country had healthier lungs.​ Is the alternative hypothesis one-sided or two-sided? one-sided two-sided one-sided or two-sided none of the above

It would be preferable for team A to play the best-of-three series, because in the longer series there is less of a chance for a weaker team to achieve the upset win multiple times.

Suppose that baseball team A is better than baseball team B. Team A is enough better that it has a 2/3 probability of beating team B in any one game, and this probability remains the same for each game, regardless of the outcomes of previous games. Suppose that team A and team B play a best-of-three series, meaning that the first team to win two games wins the series. If you are a fan of team A, would it be preferable to play a single game or a best-of-three series, or is there no difference? It would be preferable for team A to play the best-of-three series, because in the longer series there is less of a chance for a weaker team to achieve the upset win multiple times. It would be preferable for team A to play a single game, because they can play their best pitcher and probably win. It doesn't matter whether they play a single game or a best-of-three series. They should win anyway with the large probability.

True

Suppose a polling organization takes a random sample of 100 people from the population of adults in a city, (where 30% of this population wants to get rid of the penny). Then the probability is 0.015 that the sample proportion who want to get rid of the penny is less than 0.20. Stating, "If you repeatedly select a sample of 100 adults from this city and record the proportion that want to get rid of the penny for each sample, in the long run roughly 1.5% of these samples will have at most 20% of the sample wanting to get rid of the penny," would explain what it means to say "the probability of ..." while describing the random process that is repeated over and over again.

If teams A and B repeatedly play a best-of-three series, then in the long run team A will win 74.1% of those Team A has a higher chance of winning the best of three series than the 2/3 chance of winning any one game).

Suppose that baseball team A is better than baseball team B. Team A is enough better that it has a 2/3 probability of beating team B in any one game, and this probability remains the same for each game, regardless of the outcomes of previous games. Suppose that team A and team B play a best-of-three series, meaning that the first team to win two games wins the series. It turns out that the probability is 0.741 that team A would win this best-of-three series against team B. What does this probability mean? Select all that apply. All of these statements are correct. If teams A and B play a best-of-three series for 1000 times, then team A will win 741 of those series. None of these statements are correct. If teams A and B repeatedly play a best-of-three series, then in the long run team A will win 74.1% of those Team A has a higher chance of winning the best of three series than the 2/3 chance of winning any one game).

Let rolls 1 and 2 represent team B winning a game and 3-6 represent team A. Roll the die and record who wins the game until one team has won two games (two or three times). Repeat the simulation a large number of times (say 1000) and record how often team A wins divided by the number of repetitions.

Suppose that baseball team A is better than baseball team B. Team A is enough better that it has a 2/3 probability of beating team B in any one game, and this probability remains the same for each game, regardless of the outcomes of previous games. Suppose that team A and team B play a best-of-three series, meaning that the first team to win two games wins the series. Of the methods listed below, select which would be the best use of a six-sided die to approximate the probability that team A would win the best-of-three series against team B. Let rolls 1 and 2 represent team B winning a game and 3-6 represent team A. Roll the die and record who wins the game until one team has won two games (two or three times). Repeat the simulation a large number of times (say 1000) and record how often team A wins divided by the number of repetitions. Let rolls 1 and 2 represent team A winning a game and 3-6 represent team B. Roll the die and record who wins the game until one team has won two games (two or three times). Repeat the simulation for 100 times and record how often team A wins divided by the number of repetitions. Let rolls 1, 2, and 3 represent team A winning a game and 4, 5, and 6 represent team B winning a game. Roll the die and record who wins the game until one team has won two games (two or three times). Repeat the simulation 50 times and record how often team A wins divided by the number of repetitions. There is not a preferred method of the three listed.

Let rolls 1 and 2 represent team B winning a game and 3-6 represent team A. Roll the die and record who wins the game until one team has won two games (two or three times).

Suppose that baseball team A is better than baseball team B. Team A is enough better that it has a 2/3 probability of beating team B in any one game, and this probability remains the same for each game, regardless of the outcomes of previous games. Suppose that team A and team B play a best-of-three series, meaning that the first team to win two games wins the series. Which of the following describes how a six-sided die could be used to simulate one repetition of a best-of-three series between teams A and B? Let rolls 1, 2, and 3 represent team A winning a game and 4, 5, and 6 represent team B winning a game. Roll the die and record who wins the game until one team has won two games (two or three times). Let rolls 1 and 2 represent team B winning a game and 3-6 represent team A. Roll the die and record who wins the game until one team has won two games (two or three times). Let rolls 1 and 2 represent team A winning a game and 3-6 represent team B. Roll the die and record who wins the game until one team has won two games (two or three times). There is not a preferred method of the three listed.

We have little to no evidence that the long-run proportion of times Mario wins is not 50%.

Suppose two brothers named Mario and Luigi like to compete by playing a certain video game. Mario thinks he is better at this game than Luigi and sets out to prove it by keeping track of who wins. After playing the game 30 times, Mario won 18 of them (or 60%). Mario then declares that this proves he is obviously the better player. Luigi, who just finished Chapter 1 in his statistics class, realizes that perhaps he and his brother are evenly matched and just by chance Mario won 60% of the last 30 games. Luigi is going to test this by running a test of significance.​ Summarize your conclusion from your p-value. We have little to no evidence that the long-run proportion of times Luigi wins is not 40%. We have little to no evidence that the long-run proportion of times Mario wins is not 60%. We have little to no evidence that the long-run proportion of times Luigi wins is 50%. We have little to no evidence that the long-run proportion of times Mario wins is not 50%.

100

Suppose two brothers named Mario and Luigi like to compete by playing a certain video game. Mario thinks he is better at this game than Luigi and sets out to prove it by keeping track of who wins. After playing the game 30 times, Mario won 18 of them (or 60%). Mario then declares that this proves he is obviously the better player. Luigi, who just finished Chapter 1 in his statistics class, realizes that perhaps he and his brother are evenly matched and just by chance Mario won 60% of the last 30 games. Luigi is going to test this by running a test of significance.​ The p-value you found should have been greater than 0.05. Suppose the two brothers continue to compete and Mario continues to win 60% of the games. How many games will they have to play until he gets a p-value less than 0.05 after retesting? 50 80 100 40

0.2733

Suppose two brothers named Mario and Luigi like to compete by playing a certain video game. Mario thinks he is better at this game than Luigi and sets out to prove it by keeping track of who wins. After playing the game 30 times, Mario won 18 of them (or 60%). Mario then declares that this proves he is obviously the better player. Luigi, who just finished Chapter 1 in his statistics class, realizes that perhaps he and his brother are evenly matched and just by chance Mario won 60% of the last 30 games. Luigi is going to test this by running a test of significance.​ Using an appropriate applet, find the p-value using a theory-based test (one-proportion z-test; normal approximation). (Round answer to 4 decimal places; e.g. 5.2751.)p-value =

the long-run proportion of times that Mario wins

Suppose two brothers named Mario and Luigi like to compete by playing a certain video game. Mario thinks he is better at this game than Luigi and sets out to prove it by keeping track of who wins. After playing the game 30 times, Mario won 18 of them (or 60%). Mario then declares that this proves he is obviously the better player. Luigi, who just finished Chapter 1 in his statistics class, realizes that perhaps he and his brother are evenly matched and just by chance Mario won 60% of the last 30 games. Luigi is going to test this by running a test of significance.​ Which of the following describes what the parameter is that Luigi should be testing? the long-run proportion of times that Mario wins the long-run number of times that Mario loses the long-run proportion of times that Mario loses the long-run number of times that Mario wins

Null: The long-run proportion of times Mario wins is 50%.​Alt: The long-run proportion of times Mario wins is different than 50%.

Suppose two brothers named Mario and Luigi like to compete by playing a certain video game. Mario thinks he is better at this game than Luigi and sets out to prove it by keeping track of who wins. After playing the game 30 times, Mario won 18 of them (or 60%). Mario then declares that this proves he is obviously the better player. Luigi, who just finished Chapter 1 in his statistics class, realizes that perhaps he and his brother are evenly matched and just by chance Mario won 60% of the last 30 games. Luigi is going to test this by running a test of significance.​ Which of the following states the appropriate null and alternative hypotheses in the context of this study?(Hint: Luigi likes two-sided tests because he knows that will make it harder to get strong evidence that his brother is better.) Null: The long-run proportion of times Mario wins is 50%.​Alt: The long-run proportion of times Mario wins is less than 50%. Null: The long-run proportion of times Mario wins is 50%.​Alt: The long-run proportion of times Mario wins is different than 50%. Null: The long-run proportion of times Mario wins is different than 50%.​Alt: The long-run proportion of times Mario wins is 50%.

will be smaller

Suppose you are testing the hypothesis H0: π=0.50 versus Ha : π>0.50. You get a sample proportion of 0.54 and find that your p-value is 0.08. Now suppose you redid your study with each of the following changes. Now keeping the sample size the same, you take a new sample and find a sample proportion of 0.55. How will the new p-value compare to the p-value of 0.08 you first obtained? will be smaller will double will be larger won't change

will double

Suppose you are testing the hypothesis H0: π=0.50 versus Ha : π>0.50. You get a sample proportion of 0.54 and find that your p-value is 0.08. Now suppose you redid your study with each of the following changes. With your original sample, you decided to test a two sided alternative instead of Ha: π>0.50. How will the new p-value compare to the p-value of 0.08 you first obtained? won't change will be smaller will double will be larger

will be smaller

Suppose you are testing the hypothesis H0: π=0.50 versus Ha : π>0.50. You get a sample proportion of 0.54 and find that your p-value is 0.08. Now suppose you redid your study with each of the following changes. You increase the sample size and still find a sample proportion of 0.54. How will the new p-value compare to the p-value of 0.08 you first obtained? will be smaller won't change will double will be larger

The validity conditions are not met for this test since the light was green only 4 times (which is less than 10). We can also see this is a problem in the applet since the normal overlay does not match up nicely with the skewed null distribution.

Suppose you ride to school with a friend and often arrive at a certain stop light when it is red. One day she states, "It seems like this light is green only 10% of the time when we get here." You think it is more often than 10% and want to test this. You keep track of the color (green/not green) the next 20 times you go to school and find that 4 times (4/20 = 20%) the light is green when you arrive. You wish to see if your sample provides strong evidence that the true proportion of times the light is green is greater than 10%. In other words, you are testing the hypotheses H0: π = 0.10 versus Ha: π > 0.10 where π = the long-run proportion of times the light is green.Two different approaches were taken in order to yield a p-value and both are shown in the applet output.• Option 1. A simulation-based test was done and found a p-value of 0.148, showing weak evidence against the null.• Option 2. A one-proportion z-test was conducted and found a p-value of 0.068, yielding moderate evidence against the null.​ Which of the following represent the BEST reason why the p-value from option 1 is more valid. The validity conditions are not met for this test since the light was green only 4 times (which is less than 10). We can also see this is a problem in the applet since the normal overlay does not match up nicely with the skewed null distribution. The validity conditions are met for this test since the light was red only 4 times (which is less than 10). We can also see this is a problem in the applet since the normal overlay does not match up nicely with the skewed null distribution. The validity conditions are met for this test since the light was green only 4 times. We can also see this is correct in the applet since the normal overlay matches up nicely with the skewed null distribution. The validity conditions are not met for this test since the light was green only 8 times (which is close to 10). We can also see this is a problem in the applet since the normal overlay does match up nicely with the skewed null distribution.

option 1

Suppose you ride to school with a friend and often arrive at a certain stop light when it is red. One day she states, "It seems like this light is green only 10% of the time when we get here." You think it is more often than 10% and want to test this. You keep track of the color (green/not green) the next 20 times you go to school and find that 4 times (4/20 = 20%) the light is green when you arrive. You wish to see if your sample provides strong evidence that the true proportion of times the light is green is greater than 10%. In other words, you are testing the hypotheses H0: π = 0.10 versus Ha: π > 0.10 where π = the long-run proportion of times the light is green.Two different approaches were taken in order to yield a p-value and both are shown in the applet output.• Option 1. A simulation-based test was done and found a p-value of 0.148, showing weak evidence against the null.• Option 2. A one-proportion z-test was conducted and found a p-value of 0.068, yielding moderate evidence against the null.​ Which test gives a more valid p-value? Option 2 Option 1

categorical

Tennis players often spin a racquet to decide who serves first. The spun racquet can land with the manufacturer's label facing up or down. A reasonable question to investigate is whether a spun tennis racquet is equally likely to land with the label facing up or down. (If the spun racquet is equally likely to land with the label facing in either direction, we say that the spinning process is fair). Suppose that you gather data by spinning your tennis racquet 100 times, each time recording whether it lands with the label facing up or down. In this scenario, the variables would be ______________

each 100 spins

Tennis players often spin a racquet to decide who serves first. The spun racquet can land with the manufacturer's label facing up or down. A reasonable question to investigate is whether a spun tennis racquet is equally likely to land with the label facing up or down. (If the spun racquet is equally likely to land with the label facing in either direction, we say that the spinning process is fair). Suppose that you gather data by spinning your tennis racquet 100 times, each time recording whether it lands with the label facing up or down. In this scenario,_______________ are the observational units

which way the label lands

Tennis players often spin a racquet to decide who serves first. The spun racquet can land with the manufacturer's label facing up or down. A reasonable question to investigate is whether a spun tennis racquet is equally likely to land with the label facing up or down. (If the spun racquet is equally likely to land with the label facing in either direction, we say that the spinning process is fair). Suppose that you gather data by spinning your tennis racquet 100 times, each time recording whether it lands with the label facing up or down. In this scenario,_______________ is the variable

The average would increase

The monthly salaries of the three people working in a small firm are $3,500, $4,000, and $4,500. Suppose the firm makes a profit and everyone gets a $100 raise. How, if at all, would the average of the three salaries change?​ The average would stay the same. Cannot be answered without doing calculations. The average would increase. The average would decrease.

The standard deviation would stay the same.

The monthly salaries of the three people working in a small firm are $3,500, $4,000, and $4,500. Suppose the firm makes a profit and everyone gets a $100 raise. How, if at all, would the standard deviation of the three salaries change? Cannot be answered without doing calculations. The standard deviation would decrease. The standard deviation would increase. The standard deviation would stay the same.

The average would increase.

The monthly salaries of the three people working in a small firm are $3500, $4000, and $4500. Suppose the firm makes a profit and everyone gets a 10% raise, how, if at all, would the average of the three salaries change? The average would decrease. The average would increase. Cannot be answered without doing calculations. The average would stay the same.

The standard deviation would increase.

The monthly salaries of the three people working in a small firm are $3500, $4000, and $4500. Suppose the firm makes a profit and everyone gets a 10% raise, how, if at all, would the standard deviation of the three salaries change? The standard deviation would decrease. Cannot be answered without doing calculations. The standard deviation would stay the same. The standard deviation would increase.

at least as large as

The population will always be ___________ the sample

If you repeatedly record whether or not it rains for a large number of days with the same weather conditions as tomorrow, in the long run you will see rain on 30% of such days.

The probability of rain tomorrow is 0.3. Thirty percent of the region will receive rain tomorrow. If you repeatedly record whether or not it rains for a large number of days with the same weather conditions as tomorrow, in the long run you will see rain on 30% of such days. Residents of the city should prepare for about 7.2 hours (30% of 24 hours) of rain on the next day. None of these are correct.

If you repeatedly play the lottery a very large number of times, in the long run, you will win 0.1% of the times you play.

The probability of winning at a "daily number" lottery game is 1/1000. If 1000 people play the lottery, exactly one of those playing will win the lottery. Each time the lottery is played, one of 1000 people playing will win. If you repeatedly play the lottery a very large number of times, in the long run, you will win 0.1% of the times you play. All of these are correct interpretations of probability.

Random samples tend to represent the population of interest.

The reason for taking a random sample instead of a convenience sample is:​ Random samples tend to be smaller and so take less time to collect. Random samples tend to represent the population of interest. Random samples tend to be easier to implement and be successful. Random samples always have 100% participation rates.

Type I error= producer's risk, Type II error = consumer's risk

The two errors discussed in this chapter were regarded as "false alarm" and "missed opportunity." In some fields, these errors are also regarded as "consumer's risk" and "producer's risk." Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need to have a diameter of 1.65 mm—too big and they would hurt the donor (even more than usual), too small and they would rupture the red blood cells, rendering the donated blood useless. Thus, the manufacturing process would have to be closely monitored to detect any significant departures from the desired diameter. During every shift, quality control personnel take a sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected. In this hypodermic needle manufacturing process, do you think the Type I error is the consumer's risk or the producer's risk? What about the Type II error?

false

There is no way that a sample of 100 people can be representative of all adults living in the United States. True False

We have strong evidence that the long-run proportion of people who will pick the number 3 is greater than 25%

Use the following information to answer the next questions.​ It has been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.​To investigate this, a professor collected data in her class. Here is the table of responses from her students:​ Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Based on the standardized statistic, select the best conclusion that you would draw about the research question of whether students tend to have a genuine preference for the number 3 when given the choices 1, 2, 3, and 4. We have moderate evidence that the long-run proportion of people who will pick the number 3 is greater than 25% We have little to no evidence that the long-run proportion of people who will pick the number 3 is greater than 25% We have strong evidence that the long-run proportion of people who will pick the number 3 is greater than 25% We have very strong evidence that the long-run proportion of people who will pick the number 3 is greater than 25%

The mean = 0.248 and SD = 0.076.

Use the following information to answer the next questions.​ It has been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.​To investigate this, a professor collected data in her class. Here is the table of responses from her students:​ Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Find mean and the standard deviation. The mean = 0.248 and SD = 0.067. The mean = 0.284 and SD = 0.076. The mean = 0.428 and SD = 0.076. The mean = 0.248 and SD = 0.076.

0.42

Use the following information to answer the next questions.​ It has been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.​To investigate this, a professor collected data in her class. Here is the table of responses from her students:​ Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 What is the observed proportion of times students chose the number 3? What symbol should you use to represent this value? (Round answer to 2 decimal places, e.g. 52.75)

The long-run proportion of people that choose the number

Use the following information to answer the next questions.​ It has been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.​To investigate this, a professor collected data in her class. Here is the table of responses from her students:​ Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 What is the parameter of interest in the context of the study using symbol π? The long-run proportion of people that choose the number 1 The long-run proportion of people that choose the number 3 The long-run proportion of people that choose the number 2 The long-run proportion of people that choose the number 4

null: π=0.25, alternative: π>0.25

Use the following information to answer the next questions.​ It has been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.​To investigate this, a professor collected data in her class. Here is the table of responses from her students:​ Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Which of the following best describes the null hypothesis and the alternative hypothesis using the appropriate symbol? null: π=0.25, alternative: π>0.25 null: p^=0.25, alternative: p^<0.25 null: p^=0.25 , alternative: p^>0.25 null: π=0.25, alternative:

The number of standard deviations the observed proportion is above 0.25 in the null distribution.

Use the following information to answer the next questions.​ It has been conjectured that when people are asked to choose a number from the choices 1, 2, 3, and 4, they tend to choose "3" more than would be expected by random chance.​To investigate this, a professor collected data in her class. Here is the table of responses from her students:​ Chose 1- 10 Chose 2- 2 Chose 3- 14 Chose 4- 5 Which of the following best interprets the standardized statistic in the context of this study? The number of standard deviations the observed proportion is below 0.50 in the null distribution. The number of standard deviations the observed proportion is above 0.25 in the null distribution. The number of standard deviations the observed proportion is above 0.42 in the null distribution. The number of standard deviations the observed proportion is above 0.50 in the null distribution.

null hypothesis

What does H0 represent? long-run proportion (parameter) sample proportion null hypothesis alternative hypothesis

alternative hypothesis

What does Ha represent? sample proportion null hypothesis alternative hypothesis long-run proportion (parameter)

sample size

What does n represent? alternative hypothesis sample proportion sample size long-run proportion (parameter)

sample proportion

What does p^ represent? sample proportion sample size long-run proportion (parameter) null hypothesis

long-run proportion (parameter)

What does π represent? alternative hypothesis sample size long-run proportion (parameter) sample proportion

Always about the parameter only.

When stating null and alternative hypotheses, the hypotheses are:​ Always about both the statistic and the parameter. Always about the statistic only. Sometimes about the statistic and sometimes about the parameter. Always about the parameter only.

0.05 0.11

You have heard that in sports like boxing there might be some competitive advantage to those wearing red uniforms. You want to test this with your new favorite sport of chess-boxing. You randomly assign blue and red uniforms to contestants in 20 matches and find that those wearing red won 14 times (or 70%). You conduct a test of significance using simulation and get the following null distribution. (Note this null distribution uses only 100 simulated samples and not the usual 1000 or more.)​Probability of success (π): 0.5Sample size (n): 20Number of samples: 100Total = 100 Suppose you want to see if competitors wearing red win more than 50% of the matches in the long run, so you test H0: π= 0.50 versus Ha: π > 0.50. What is your p-value based on the above null distribution? Suppose you now want to see if competitors wearing either red or blue have an advantage, so you test H0: π= 0.50 versus Ha: π ≠ 0.50. What is your p-value now based on the above null distribution?

True

You should not take a random sample of more than 5% of the population size. True False

strong

____Love, firstA recent study (Ackerman, Griskevicius, and Li, 2011) examined expressions of commitment between two partners in a committed romantic relationship. One aspect of the study involved 47 heterosexual couples who are part of an online pool of people willing to participate in surveys. These 47 couples were asked about which person was the first to say "I love you." For 7 of those couples, the two people disagreed about the answer to this question. But both people agreed for the other 40 couples, so those 40 responses were included in the analysis. Previous studies have suggested that males tend to say "I love you" first.​​ The small p-value gives us ____________ evidence that for more than 50% of couples the man said " I love you" first.

Charlene - most extreme range of values

​Consider three students with the following distributions of 24 quiz scores: Amanda: 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,8, 8, 8, 8, 8, 8 Barney: 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8,8, 9, 9, 9, 9, 10 Charlene: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 10, 10,10, 10, 10, 10, 10, 10, 10, 10​ Without bothering to do any calculations, which student has the largest standard deviation of quiz scores? Barney - middle range of values You cannot decide without performing the calculations for comparison. Charlene - most extreme range of values Amanda - more consistency in values

Amanda - more consistency in values

​Consider three students with the following distributions of 24 quiz scores: Amanda: 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,8, 8, 8, 8, 8, 8 Barney: 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8,8, 9, 9, 9, 9, 10 Charlene: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 10, 10,10, 10, 10, 10, 10, 10, 10, 10​ ​ Without bothering to do any calculations, which student has the smallest standard deviation of quiz scores? Barney - middle range of values Charlene - most extreme range of values Amanda - more consistency in values You cannot decide without performing the calculations for comparison.

546

​Dwyane Wade of the Miami Heat hit 569 of his 1093 field goal attempts in the 2012/2013 season for a shooting percentage of 52.1%. Over the lifetime of Dwyane's career, can we say that Dwyane is more likely than not to make a field goal? Of the values given, what would be the most typical value of the number of heads from a repetition of 1093 coin flips? 546 521 500 569

parameter

​Dwyane Wade of the Miami Heat hit 569 of his 1093 field goal attempts in the 2012/2013 season for a shooting percentage of 52.1%. Over the lifetime of Dwyane's career, can we say that Dwyane is more likely than not to make a field goal? What statistical term is given to the long-run proportion of Dwyane making a field goal? sample size parameter statistic chance model

statistic

​Dwyane Wade of the Miami Heat hit 569 of his 1093 field goal attempts in the 2012/2013 season for a shooting percentage of 52.1%. Over the lifetime of Dwyane's career, can we say that Dwyane is more likely than not to make a field goal? What statistical term is given to the value 52.1%? statistic sample size parameter chance model

1093

​Dwyane Wade of the Miami Heat hit 569 of his 1093 field goal attempts in the 2012/2013 season for a shooting percentage of 52.1%. Over the lifetime of Dwyane's career, can we say that Dwyane is more likely than not to make a field goal? When simulating possible outcomes assuming the chance model, how many times would you flip a coin for one repetition of the 2012/2013 season? 1000 52 569 1093

the proportion of heads out of 1093 flips

​Dwyane Wade of the Miami Heat hit 569 of his 1093 field goal attempts in the 2012/2013 season for a shooting percentage of 52.1%. Over the lifetime of Dwyane's career, can we say that Dwyane is more likely than not to make a field goal? With each set of flips, what would you keep track of? the total number of tails minus the total number of heads if 569 heads were recorded in that set the number of times the proportion of heads is greater than 52.1% the proportion of heads out of 1093 flips

We have very strong evidence that the long-run proportion of times that a player starts with rock is different from 33%.

​Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock. We investigated some results of the game rock-paper-scissors, the researchers had 119 people play rock paper- scissors against a computer. They found 66 players (55.5%) started with rock, 39 (32.8%) started with paper, and 14 (11.8%) started with scissors. We want to see if players start with rock with a probability that is different from 1/3.​ Summarize the conclusion from the p-value. We have strong evidence that the long-run proportion of times that a player starts with rock is 33%. We have very weak evidence that the long-run proportion of times that a player starts with rock is different from 33%. We have very strong evidence that the long-run proportion of times that a player starts with rock is different from 33%. We have no evidence that the long-run proportion of times that a player starts with rock is different from 33%.

0.00

​Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock. We investigated some results of the game rock-paper-scissors, the researchers had 119 people play rock paper- scissors against a computer. They found 66 players (55.5%) started with rock, 39 (32.8%) started with paper, and 14 (11.8%) started with scissors. We want to see if players start with rock with a probability that is different from 1/3.​ Using an appropriate applet, find the p-value using a theory-based test (one-proportion z-test; normal approximation). (Round your answer to the nearest whole number.)

Null: The long-run proportion of times that a player starts with rock is 33%.Alt: The long-run proportion of times that a player starts with rock is different from 33%.

​Have you ever played rock-paper-scissors (or Rochambeau)? It's considered a "fair game" in that the two players are equally likely to win (like a coin toss). Both players simultaneously display one of three hand gestures (rock, paper, or scissors), and the objective is to display a gesture that defeats that of your opponent. The main gist is that rocks break scissors, scissors cut paper, and paper covers rock. We investigated some results of the game rock-paper-scissors, the researchers had 119 people play rock paper- scissors against a computer. They found 66 players (55.5%) started with rock, 39 (32.8%) started with paper, and 14 (11.8%) started with scissors. We want to see if players start with rock with a probability that is different from 1/3.​ Which of the following states the appropriate null and alternative hypotheses in the context of this study, first in words and then in symbols? Null: The long-run proportion of times that a player starts with rock is 33%.Alt: The long-run proportion of times that a player starts with rock is more than 33%. Null: The long-run proportion of times that a player starts with rock is 33%.Alt: The long-run proportion of times that a player starts with rock is different from 33%. Null: The long-run proportion of times that a player starts with rock is 33%.Alt: The long-run proportion of times that a player starts with rock is less than 33%. Null: The long-run proportion of times that a player starts with rock is 50%.Alt: The long-run proportion of times that a player starts with rock is different from 50%.

gender, washed hands, and location

​In August of 2005, researchers for the American Society for Microbiology and the Soap and Detergent Association monitored the behavior of more than 6,300 users of public restrooms. They observed people in public venues such as Turner Field in Atlanta and Grand Central Station in New York City. For each person they kept track of the person's sex and whether or not the person washed his or her hands along with the person's location. Which of the following are the variables recorded on each observational units? gender and location only washed hands, location, and public restroom users gender, washed hands, and public restroom users gender, washed hands, and location

incorrect a likely

​​A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups. Suppose that I try to discern whether tea or milk is poured first for 8 cups and make the correct identification 5 times. I say "5 out of 8 is more than half, so one must conclude that I'm doing better than random guessing." This conclusion is____________ because 5 out of 8 is _____________ result if someone id just guessing

Result provides strong evidence that the person actually has ability better than random guessing.

​​A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups. Suppose that I try to discern whether tea or milk is poured first for 8 cups and make the correct identification 5 times. Now suppose that someone gets 14 correct out of 16 cups. Applet inputs are: probability of success (π) = 0.5, sample size (n) = 16, number of samples = 1000. Applet output suggests that 14 out of 16 is a fairly unlikely result (~2 out of 1000 times). Select the best conclusion that you would draw that the person actually has better ability than random guessing. Result provides strong evidence that the person actually has ability better than random guessing. Result provides weak evidence that the person actually has ability better than random guessing. Result provides conclusive evidence that the person actually has ability better than random guessing. Result provides no evidence that the person actually has ability better than random guessing.

True

​​A famous (in statistical circles) study involves a woman who claimed to be able to tell whether tea or milk was poured first into a cup. She was presented with eight cups containing a mixture of tea and milk, and she correctly identified which had been poured first for all eight cups. Suppose that I try to discern whether tea or milk is poured first for 8 cups and make the correct identification 5 times. With regards to the study on 8 cups of tea and milk, it is plausible (believable) that you are not guessing. True False