Statistics Ch2
(b) Find the standardized statistic to investigate whether the data provide evidence that the average number of hours per day Cal Poly students spend watching TV is different from 2.84 hours. Round answer to 2 decimal places, e.g. 0.29. Standardized statistic=
.86
(c) Use the applet to take at least 10,000 samples of size 27 from the data to develop a bootstrap distribution of sample means. Which of the following is the closest to the standard deviation of your distribution of sample means?
2.346
Identify two statistics that the student could use to summarize the variable.
mean or median
(b) μ=10, σ=4, n=100
mean=10 sd=.4
In a November 1992 survey, the Roper Organization asked American adults, "Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened?" The results were very surprising and widely discussed. Of the 992 adults surveyed, 22% responded that it's possible that this never happened, and 12% responded that they did not know. Therefore, only 66% of the respondents expressed certainty that the Holocaust did happen. What is wrong with the wording of this question that produced such surprising (and it was later shown) erroneous results?
"Impossible that it never happened" contains a double negative
(d) Using the standard deviation from your bootstrap distribution of sample means, what is the standardized statistic for the data. In other words, how many standard deviations is the sample mean away from 0? Based on the standardized statistic, what sort of conclusion can you make? Choose the best among the following statements.
(6.296 - 0)/2.346 = 2.68. Because the standardized statistic is more than 2, we have strong evidence that the mean score is different (greater) than 0, or people, on average, pick faces that are better looking than their own in the long run.
Marriage agesA student went to the local county courthouse in Pennsylvania to gather data on ages of soon-to-be husbands and wives who had recently applied for marriage licenses. He gathered age data on a sample of 100 couples and calculated the difference in age (husband-wife) for each couple. The student wanted to see whether the average difference in ages (husband-wife) is greater than 0. In other words, are husbands older than their wives, on average? The results can be found in the file MarriageAgesDiff. Use the One Mean applet to take at least 10,000 samples from the MarriageAges data to develop a bootstrap sampling distribution for the mean. Which of the following is the closest to the standard deviation of your distribution of sample means?
.507
(c) Which of the following is the closest to the p-value for this test?
.02
(e) Which of the following is the closest to the p-value for this test?
0.50
(c) How many standard deviations is the sample proportion of 1,523/2,216 above 0.592? Round answer to 2 decimal places, e.g. 0.23. The sample proportion of 1,523/2,216 is ___standard deviations above 0.592.
9.16
A t-distribution is shaped like a normal distribution but is:
A bit more spread out and more observations in the tails than a normal distribution.
Identify one graph that the news program could use to summarize the variable.
Bar graph
Is the variable categorical or quantitative?
Categorical
To which population, if any, are you comfortable drawing your conclusion?
Comfortable generalizing to a population like the one that participated in the survey - watchers of the TV news program who were motivated enough to participate.
Identify one graph that the news program could use to summarize the variable.
Dot plot
Larger samples are always better than smaller samples, regardless of how the sample was collected.
False
Write the appropriate hypotheses using appropriate symbols to test whether the average diameter of needles from the manufacturing process is different from the desired value.Choose the answer from the menu in accordance to the question statement H0: µ = 1.65 mm Ha: µ < 1.65 mmH0: µ = 1.65 mm Ha: µ > 1.65 mmH0: µ = 1.65 mm Ha: µ ≠ 1.65 mm
H0: µ = 1.65 mm Ha: µ ≠ 1.65 mm
For the following table, complete the column on the right to draw parallels between the simulation and the real study: Simulation vs Real study
One repetition= a random sample of 35 needles Null model= population mean of diameter is 1.65 mm Statistic=average diameter of needles in the sample
(b) What is the standard deviation of sample proportions when you take samples of 2,216 from the population of all eligible voters, where the proportion that voted in the population is 0.592? Round answer to 4 decimal places, e.g. 0.2358.
SD of sample proportions is .0104
(b) Suppose you wanted to test the hypotheses:H0: Students drink 7 cups of coffee per week, on average (μ=7).Ha: Students do not drink 7 cups of coffee per week, on average (μ≠7).Develop a bootstrap sampling distribution for this. What is the standard deviation of your distribution of the bootstrap sampling distribution? Round answer to 1 decimal place, e.g. 2.9.
SD=1.4
(e) Shift the data so its mean is as close to 0 as possible. Using the shifted bootstrap sampling distribution, what is your p-value? Using your p-value, do you come to the same conclusion as you did in part (d)?
Since the p-value is less than 0.05, we come to the same conclusion.
How cool are you?The data set MaleTemps (found on the textbook website) consists of 65 body temperatures from healthy male volunteers aged 18 to 40 that were participating in vaccine trials. Put this data set into the Descriptive Statistics applet and answer the following questions. Is the distribution of temperatures symmetric, skewed to the left, skewed to the right, or something else? The distribution is something else. The distribution is skewed to the right. The distribution is fairly symmetric. The distribution is skewed to the left. Would you think the mean temperature for the 65 males in the study is about the same as the median, higher than the median, or lower than the median? mean ≈ median mean < median mean > median
The distribution is fairly symmetric. mean ≈ median
In the Sampling Words applet with the Gettysburg Address using the variable length, the numbers on the horizontal axis of the graph for the population distribution represent the length of the words - a quantitative variable. When you start taking samples of size 10, do the numbers on the horizontal axes of the two other graphs also represent the length of the words? If not, what do they represent? Are they all quantitative variables?
The horizontal axis of the graph of the most recent sample is the length of the words, but the horizontal axis of the graph of the statistic is the mean length of the words in a sample of 10 words. Both of these are quantitative.
How many standard deviations is the sample proportion of 1,523/2,216 above 0.592? Round answer to 2 decimal places, e.g. 0.23.
The sample proportion of 1,523/2,216 is 9.16 standard deviations above 0.592.9
In Exploration 2.1, you used an applet to take many samples of words from the Gettysburg Address, found the proportion of short words in each sample, and then created a distribution of the sample proportions. To reduce the standard deviation of the distribution of sample proportions, you could have:
Used a larger sample size.
The population will always be BLANK as the sample
as large as
Read FAQ 2.3.3 to learn about Type I and Type II errors in order to be able to complete this exercise. Later in the book you will encounter many hypotheses of the following type: H0: New treatment is no better than current treatment. Ha: New treatment is better than current treatment. (a) Describe what Type I error means in this context. We____strong evidence the new treatment is better, when it actually ___. (b) Describe what Type II error means in this context. We ___have strong evidence the new treatment is better, when it actually ___.
have, is not, do not have, is
Identify one graph that the polling agency could use to summarize the variable. Dot plot Line graph Circle graph Scatter plot
dot plot
Identify one graph that the student could use to summarize the variable.
dotplot
(d) Is the General Social Survey (GSS) result still significantly larger than the actual result? Choose the best among the following statements. Because the sample proportion is ____ 0.592, it isis not significantly larger than the actual result. Results like this are very ___ to happen by chance.
more than 3 SD above, is, unlikely
Is the variable categorical or quantitative?
quantitative
To which population, if any, are you comfortable drawing your conclusion? Why?
students at the school or similar to the ones in the study
n order to estimate the typical amount of TV watched per day by students at her school of 1,000 students, a student has all of the students in her statistics class (30 students) take a short survey. In the survey the student asked students whether or not they watched at least 10 minutes of TV yesterday. The student found that 21 of 30 students reported watching at least 10 minutes of TV yesterday. The student wishes to test whether there is evidence that more than 50% of students at the school watched at least 10 minutes of TV yesterday. Evaluate the strength of evidence for this hypothesis. Calculating the p-value for the hypothesis using a simulation-based approach gives a p-value of 0.0214. Based on the p-value evaluate the strength of evidence and state a conclusion about the TV watching among students yesterday.
there is strong evidence more then 10 minutes a day
When assigning symbols to statistics and parameters, which of the following is correct? (Choose all that are correct.)
x bar is the sample mean, μ is the population mean. p^ is the sample proportion, π is the population proportion.
(d) Using the standard deviation from your bootstrap distribution of sample means, what is the standardized statistic for the data. In other words, how many standard deviations is the sample mean away from 0? Based on the standardized statistic, what sort of conclusion can you make? Choose the best among the following statements. (6.296 - 0)/2.346 = 2.68. Because the standardized statistic is more than 2, we have strong evidence that the mean score is different (greater) than 0, or people, on average, pick faces that are better looking than their own in the long run. (6.296 - 0)/4.547 = 1.38. Because the standardized statistic is less than 2, we do not have strong evidence that the mean score is different (greater) than 0, or people, on average, pick faces that are better looking than their own in the long run. (6.296 - 0)/6.239 = 1.01. Because the standardized statistic is less than 2, we do not have strong evidence that the mean score is different (greater) than 0, or people, on average, pick faces that are better looking than their own in the long run. (6.296 - 0)/7.100 = 0.89. Because the standardized statistic is less than 2, we do not have strong evidence that the mean score is different (greater) than 0, or people, on average, pick faces that are better looking than their own in the long run.
(6.296 - 0)/2.346 = 2.68. Because the standardized statistic is more than 2, we have strong evidence that the mean score is different (greater) than 0, or people, on average, pick faces that are better looking than their own in the long run.
In Example 2.1, you saw that the percentage of people who said they voted in the 2016 Presidential election from the General Social Survey (GSS) (69.8%) was significantly different than the percentage of people that actually voted in that election (59.2%). You also saw that this difference came from a nonsampling concern. Some people are not honest when they are answering a question the answer to which can be perceived as undesirable - like saying they did not vote. Let's take another look at that example. From the GSS, we saw that 1,523 said they voted out of 2,181 people that were eligible to vote and answered yes or no to the question of whether or not they voted. Thirty-five people were asked this question and either did not respond or said that they could not remember if they voted. Let's add these people to the total number that were asked the question. So our new proportion is 1,523 said they voted out of 2,216 eligible voters that were asked the question.
(a) Is the new proportion (1,523/2,216) closer to the actual proportion that voted than what you saw in the example? The new proportion of 0.687is closer not closer to the proportion that actually voted.
Identify the numeric value of the statistic corresponding to the above parameter, as found in the television news survey. Give your answer as a proportion.
.82
A student went to the local county courthouse in Pennsylvania to gather data on ages of soon-to-be husbands and wives who had recently applied for marriage licenses. He gathered age data on a sample of 100 couples and calculated the difference in age (husband-wife) for each couple. The student wanted to see whether the average difference in ages (husband-wife) is greater than 0. In other words, are husbands older than their wives, on average? The results can be found in the file MarriageAges. Shift the sample data appropriately and find a p-value. (Choose the option that is the closest to your answer.)
0.0001
(b) What is the standard deviation of sample proportions when you take samples of 2,216 from the population of all eligible voters, where the proportion that voted in the population is 0.592? Round answer to 4 decimal places, e.g. 0.2358. SD of sample proportions is...
0.0104
Suppose you have a large bucket containing 40% red gummy bears and 60% green gummy bears. You take many, many random samples of 25 gummy bears and each time note the proportion that are red. From this, you create a distribution of all your sample proportions of red gummy bears. You should expect the mean of your distribution of sample proportions to be approximately which of the following? 0.40 0.50 0.60 10
0.40
For two years, one of the authors asked his students how long they slept the previous night. He now has 255 results with a mean of 7.12 hours and a standard deviation of 1.59 hours. This distribution of sleep times is fairly symmetric. We will call these 255 sleep times a population and then take many, many random samples of 10 sleep times from this population. From this, we create a distribution of the sample means from all the resulting samples. We should expect the standard deviation of this distribution of sample means to be approximately which of the following?
0.50
Television news surveyIn 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 numeric value of the statistic corresponding to the above parameter, as found in the television news survey. Give your answer as a proportion.
0.82
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 random sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected. For now, suppose that a "problem" is when the sample average diameter turns out to be statistically significantly different from the target of 1.65 mm. Consider the investigation of the manufacturing process that is producing hypodermic needles. Describe how you can conduct a simulation-based test of significance to investigate whether the data provide evidence that the average diameter of needles produced by this manufacturing process is different from 1.65 mm. Select steps on how one would find a p-value.1. You would have to fabricate a large data set to represent the population of needles with the variability similar to that of the sample data and a mean of 1.65.2. You would have to fabricate a large data set to represent the population of needles with the variability and mean similar to that of the sample data.3. From that data you would take a sample of 35 and find its mean. Repeat this at least 1000 times to develop a null distribution.4. To determine the p-value, determine the proportion of simulated statistics that are at least as extreme as or more extreme than 1.64.
1, 3 and 4
(c) Use the applet to take at least 10,000 samples of size 27 from the data to develop a bootstrap distribution of sample means. Which of the following is the closest to the standard deviation of your distribution of sample means? 2.346 4.547 6.239 7.100
2.346
Students were asked how many cups of coffee they typically drink in a week. The results for 15 students is in the file Coffee. Put the data into the One Mean applet using the Bootstrapping option and answer the following. (a) What is the mean of the data? Round answer to 1 decimal place, e.g. 2.9.
3.8
A zoologist at a large metropolitan zoo is concerned about a potential new disease present among the 243 sharks living in the large aquarium at the zoo. The zoologist takes a random sample of 15 sharks from the aquarium, temporarily removes the sharks from the tank, and tests them for the disease. He finds that 3 of the sharks have the disease.The zoologist wishes to test whether there is evidence that less than one-fourth of the sharks in the aquarium are diseased. Evaluate the strength of evidence for this hypothesis. Find the p-value for the hypothesis using a simulation-based approach. 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. A theory-based approach is reasonable since the sample size is less than 5% of the population. A theory-based approach is not reasonable since the p-value does not match the p-value found using a simulation-based approach. A theory-based approach is reasonable since the p-value is the same as the p-values found using a simulation-based approach. A theory-based approach is not reasonable since there were only 3 sharks with the disease. We need at least 10.
A theory-based approach is not reasonable since there were only 3 sharks with the disease. We need at least 10.
In order to investigate how many hours a day full-time students at their school tend to spend on course work outside of regularly scheduled class time, a statistics student takes a random sample of 150 students from their school by randomly choosing names from a list of all full-time students at their school that semester. The student finds that the average reported daily study hours among the 150 students is 2.23 hours. Identify the population of interest. Choose the answer from the menu in accordance to the question statement Random sample of the students at the school.All students in the U.S.All full-time students at the school.
All full-time students at the school.
(d) Is the General Social Survey (GSS) result still significantly larger than the actual result? Choose the best among the following statements.
Because the sample proportion is more than 3 SD above it is significantly larger than the actual result. Results like this are very unlikely to happen by chance.
Scores on a recent statistics exam had a mean of 82.7 and a median of 87. If your score on this exam was an 84, did more students in the class have scores higher than yours or lower than yours?
Because your score of 84 is below the median of 87, more students had exam scores higher than yours.
Describe what a Type II error would be in this study.
Buzz is not guessing but we do not determine he is not guessing
Identify two statistics that the polling agency could use to summarize the variable. Mean or Median Median or Mode Mean or proportions Median or proportions
Mean or Median
The applet output shown below has three distributions that involve sampling words from the Gettysburg Address like what was done in Exploration 2.2 when we focused on the length of the words. Choose from the following list to describe each distribution and put the appropriate letters in the blanks below. A. A distribution of proportions of short words taken from many, many random samples. B. A distribution of mean word lengths taken from many, many random samples. C. A distribution of word lengths from one sample of 20 words. D. A distribution of word lengths from many, many samples. E. The population distribution of word lengths. F. A distribution of the proportion of short words (or not) from one sample of size 25.
E, C, B
The applet output shown below has three distributions that involve sampling words from the Gettysburg Address like what was done in Exploration 2.1 when we focused on whether a word was short or not. Choose from the following list to describe each distribution and put the appropriate letters in the blanks below. A. A distribution of proportions of short words taken from many, many random samples. B. A distribution of mean word lengths taken from many, many random samples. C. A distribution of the proportion of short words (or not) from one sample of size 25. D. A distribution of word lengths from many, many samples. E. The population distribution of word lengths. F. The population distribution of the proportion of short words (or not).
F= no, yes bar graph C=no, yes dot plot A=number bar graph
A theory-based approach would be reasonable for this data, and would result in a similar p-value to the p-value you found with a simulation-based approach.
False
The two distributions below are the mean length of words from samples of 10 words and 30 words from the Gettysburg Address. Which distribution comes from samples of size 10 and which from 30? Choose the best among the following statements. Graph A is a distribution of sample means from samples of size 10; we know this because it is the distribution with the smaller standard deviation. Graph A is a distribution of sample means from samples of size 30; we know this because it is the distribution with the smaller standard deviation. Graph A is a distribution of sample means from samples of size 10; we know this because it is the distribution with the mean closer to the population mean. Graph A is a distribution of sample means from samples of size 30; we know this because it is the distribution with the mean closer to the population mean. There is not enough information to answer.
Graph A is a distribution of sample means from samples of size 30; we know this because it is the distribution with the smaller standard deviation.
Do people think they look different than they actually do? In particular, do they think they look better? Researchers Epley and Whitchurch (2008) tried to answer this question by taking pictures of 27 subjects (both male and female). They then had the picture of each subject's face morphed with that of someone that was thought to be better looking. The images were morphed in 10% increments so that the first morph was 90% the subject and 10% the better-looking person, the second was 80% subject and 20% better-looking person. This continued until the face was 50% of each person. They did the same thing with a picture of a person that was thought to be not good looking. The researchers then had 11 pictures for each subject, one of the actual subject and 10 with various morphings. Each subject was presented the 11 pictures, in random order, and asked which was the actual picture of their face. If they picked one that was composed of 20% of the better-looking face, their score was 20. If they picked one that was composed of 10% of the worse-looking face their score was -10. Of course, if they picked the picture of their own face, their score was 0. The results from the 27 subjects are in the file Morphing. Answer the following questions to complete a test of significance to determine whether there is strong evidence that, on average, people tend to pick a face that is different from their own. (a) What are the appropriate null and alternative hypotheses for this study?
H0: People tend to pick their own face, on average (μ=0).Ha: People tend to pick a face that is different than theirs, on average
Do people think they look different than they actually do? In particular, do they think they look better? Researchers Epley and Whitchurch (2008) tried to answer this question by taking pictures of 27 subjects (both male and female). They then had the picture of each subject's face morphed with that of someone that was thought to be better looking. The images were morphed in 10% increments so that the first morph was 90% the subject and 10% the better-looking person, the second was 80% subject and 20% better-looking person. This continued until the face was 50% of each person. They did the same thing with a picture of a person that was thought to be not good looking. The researchers then had 11 pictures for each subject, one of the actual subject and 10 with various morphings. Each subject was presented the 11 pictures, in random order, and asked which was the actual picture of their face. If they picked one that was composed of 20% of the better-looking face, their score was 20. If they picked one that was composed of 10% of the worse-looking face their score was -10. Of course, if they picked the picture of their own face, their score was 0. The results from the 27 subjects are in the file Morphing. Answer the following questions to complete a test of significance to determine whether there is strong evidence that, on average, people tend to pick a face that is different from their own. (a) What are the appropriate null and alternative hypotheses for this study? H0: People tend to pick their own face (x¯=0).Ha: People tend to pick a face that is different than theirs (x¯≠0). H0: People tend to pick their own face (μ=0).Ha: People tend to pick a face that is different than theirs (μ≠0). H0: People tend to pick their own face, on average (x¯=0).Ha: People tend to pick a face that is different than theirs, on average (x¯≠0). H0: People tend to pick their own face, on average (μ=0).Ha: People tend to pick a face that is different than theirs, on average(μ≠0)
H0: People tend to pick their own face, on average (μ=0).Ha: People tend to pick a face that is different than theirs, on average(μ≠0)
In the same study as was mentioned in the previous two exercises, data were also collected on 65 healthy female volunteers aged 18 to 40 that were participating in the vaccine trials. The data set FemaleTemps consisting of body temperatures from the 65 females is available from the textbook website. You will use the data to investigate whether the average body temperature of healthy adult females is different from 98.6°F What are the appropriate null and alternative hypotheses for this study? H0: μ=98.6°F,Ha: μ≠98.6°F H0: μ=98.6°F,Ha: μ>98.6°F H0: μ=98.6°F,Ha: μ<98.6°F eTextbook and Media
H0: μ=98.6°F,Ha: μ≠98.6°F
Write the appropriate hypotheses using appropriate symbols to test whether the average diameter of needles from the manufacturing process is different from the desired value.
H0=1.65 Ha does not equal 1.65
In order to estimate the proportion of all likely voters who will likely vote for the incumbent in the upcoming city's mayoral race, a random sample of 267 likely voters is taken, finding that 65% state they will likely vote for the incumbent. The poll also asked voters to report the amount of time that the respondent spent reading or learning about local politics over the past week. The poll finds that, on average, respondents have spent 42 minutes learning or reading about local politics over the past week. Identify the variable measured on each likely voter. Choose the answer from the menu in accordance to the question statement All likely voters in the city. How long people spend reading or learning about local politics. Whether or not the person is likely to vote in the upcoming local election.
How long people spend reading or learning about local politics
To which population, if any, are you comfortable drawing your conclusion? Why? Choose the answer from the menu in accordance to the question statement I am comfortable generalizing my conclusion to all people in the U.S.I am comfortable generalizing my conclusion to all college students in the U.S.I am comfortable generalizing my conclusion to all students at her school.I could generalize my conclusion to students at her school similar to the ones in the study. A theory-based approach would be reasonable for this data, and would result in a similar p-value to the p-value you found with a simulation-based approach. True False
I could generalize my conclusion to students at her school similar to the ones in the study. False
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.Choose the answer from the menu in accordance to the question statement Buzz is not guessing, and we determine that he is not guessing.Buzz is guessing, but we determine that he is not guessing.Buzz is guessing, and we do not determine that he is not guessing.Buzz is not guessing, but we do not determine that he is not guessing. Describe what a Type II error would be in this study.Choose the answer from the menu in accordance to the question statement Buzz is guessing, and we do not determine that he is not guessing.Buzz is guessing, but we determine that he is not guessing.Buzz is not guessing, and we determine that he is not guessing.Buzz is not guessing, but we do not determine that he is not guessing.
I=Buzz is guessing, but we determine that he is not guessing II=Buzz is not guessing, but we do not determine that he is not guessing.
In order to estimate the typical amount of TV watched per day by students at her school of 1,000 students, a student has all of the students in her statistics class (30 students) take a short survey, finding that, on average, students in her statistics class report watching 1.2 hours of television per day.
Identify the variable measured on each student. the number of hours of TV watched per day
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 random sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected. For now, suppose that a "problem" is when the sample average diameter turns out to be statistically significantly different from the target of 1.65 mm.
Identify the variable of interest and whether the variable is categorical or quantitative.The diameter of needles and it is quantitative.
Why should we let random chance dictate our sample selection? Use the example of a famous study from the 1960s that explored whether two dolphins (Doris and Buzz) could communicate abstract ideas. 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." About Doris and Buzz, explain where randomization could come into play in the study design. In the Doris and Buzz example, Dr. Bastian randomly determines whether the light would flash. In the Doris and Buzz example, Dr. Bastion randomly determines which button to give the dolphins. In the Doris and Buzz example, Dr. Bastion randomly determines which dolphin is shown the light. In the Doris and Buzz example, Dr. Bastion randomly determines whether the light is turned on.
In the Doris and Buzz example, Dr. Bastian randomly determines whether the light would flash.
In Example 2.1, you saw that the percentage of people who said they voted in the 2016 Presidential election from the General Social Survey (GSS) (69.8%) was significantly different than the percentage of people that actually voted in that election (59.2%). You also saw that this difference came from a nonsampling concern. Some people are not honest when they are answering a question the answer to which can be perceived as undesirable - like saying they did not vote. Let's take another look at that example. From the GSS, we saw that 1,523 said they voted out of 2,181 people that were eligible to vote and answered yes or no to the question of whether or not they voted. Thirty-five people were asked this question and either did not respond or said that they could not remember if they voted. Let's add these people to the total number that were asked the question. So our new proportion is 1,523 said they voted out of 2,216 eligible voters that were asked the question.
Is the new proportion (1,523/2,216) closer to the actual proportion that voted than what you saw in the example? The new proportion of .6870is closer to the proportion that actually voted.
Correct answer iconYour answer is correct. (b) The dotplot below shows the 65 body temperatures. Based on this dotplot, does it appear the average body temperature is different than 98.6°F? Choose the best among the following statements. Yes, because not all the points are equal to 98.6°F. No, because the average of the maximum temperature and the minimum temperature is close to 98.6°F. It is hard to tell, because there is a lot of variability in the data.
It is hard to tell, because there is a lot of variability in the data.
We can reduce the possibility of having bias in a study by: Increasing the sample size. Making sure our sample is a simple random sample. Using a one-sided alternative hypothesis instead of a two-sided alternative hypothesis. Conducting a theory-based test instead of a simulation-based test.
Making sure our sample is a simple random sample.
Identify two statistics that the news program could use to summarize the variable.
Mean or Median
(d) Now suppose the person that reported drinking 20 cups of coffee per week should have actually been 40 cups. Change the 20 to 40 in the data set and redo the simulation. Give the sample mean and the standard deviation of the bootstrap sampling distribution.
Mean=5.133 SD=2.5
Read FAQ 2.3.2 and answer the following question. How are degrees of freedom, t-distributions, and normal distributions related?Choose the answer from the menu in accordance to the question statement The more degrees of freedom, the less the t-distribution looks like a normal distribution.More degrees of freedom, the more the t-distribution looks like a normal distribution.
More degrees of freedom, the more the t-distribution looks like a normal distribution.
In order to estimate the typical amount of TV watched per day by students at her school of 1,000 students, a student has all of the students in her statistics class (30 students) take a short survey. In the survey the student asked students whether or not they watched at least 10 minutes of TV yesterday. The student found that 21 of 30 students reported watching at least 10 minutes of TV yesterday. The student wishes to test whether there is evidence that more than 50% of students at the school watched at least 10 minutes of TV yesterday. State the null and alternative hypotheses for this test.
Null: Choose your answer; Null Less than 50% of the students at the school watched at least 10 minutes of TV yesterday. Alternative: More than 50% of the students at the school watched at least 10 minutes of TV yesterday.
The administration at a local high school is considering building a new gym. In order to find out how the student body feels about this, a student organization decides to conduct a survey of the students. Which of the following sampling methods should be unbiased? Survey random students who are leaving after school sports practices. Survey random students who are going to watch a basketball game at the high school. Obtain a list of all seniors, randomly select students from the list, and survey the students selected. Obtain a list of all students attending the high school, randomly select students from the list, and survey the students selected.
Obtain a list of all students attending the high school, randomly select students from the list, and survey the students selected.
In most statistical studies the Choose your answer is unknown and the Choose your answer is known.
Paremeter, statistics
Identify one statistic that the news program could use to summarize the variable.
Proportion
The reason for taking a random sample instead of a convenience sample is:
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 represent the population of interest. Random samples always have 100% participation rates. Random samples tend to be smaller and so take less time to collect. Random samples tend to be easier to implement and be successful.
Random samples tend to represent the population of interest.
The Gettysburg Address has 268 words and the average word length is 4.29 letters. If we are going to randomly choose words from that speech, which of the following is least likely to happen?
Randomly picking a word from the Gettysburg Address and have it be 3.29 to 5.29 letters in length.
The Gettysburg Address has 268 words and the average word length is 4.29 letters. If we are going to randomly choose words from that speech, which of the following is least likely to happen? Randomly picking a word from the Gettysburg Address and have it be 3.29 to 5.29 letters in length. Randomly picking 5 words from the Gettysburg Address and have the mean be 3.29 to 5.29 letters in length. Randomly picking 10 words from the Gettysburg Address and have the mean be 3.29 to 5.29 letters in length.
Randomly picking a word from the Gettysburg Address and have it be 3.29 to 5.29 letters in length.
Why should we let random chance dictate our sample selection?Use the example of a famous study from the 1960s that explored whether two dolphins (Doris and Buzz) could communicate abstract ideas. 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."To examine Dr. Bastian's findings, you created a chance model of flipping a coin to determine whether the dolphins were choosing the correct button by random chance or because they understood the commands.Explain where randomization occurs in your chance model but may not be truly random chance in the study. Randomness occurs in the chance model by flipping a coin to determine if Buzz would communicate with Doris. In reality, Buzz may not have a constant probability of communicating with Doris. Randomness occurs in the chance model by flipping a coin to determine if Buzz would push the correct button if he was just guessing (a constant probability). In reality, Buzz may not have a constant probability of choosing the correct button. He may be learning along the way, he may get tired, or his stomach may get full of fish.
Randomness occurs in the chance model by flipping a coin to determine if Buzz would push the correct button if he was just guessing (a constant probability). In reality, Buzz may not have a constant probability of choosing the correct button. He may be learning along the way, he may get tired, or his stomach may get full of fish.
Do you believe that the average hours of television per day in the sample are likely less than, similar to, or greater than the average hours of television watched per day in the population? Greater than that of students in the entire school. Less than that of students in the entire school. Similar to that of students in the entire school.
Similar to that of students in the entire school.
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 increase. The average would stay the same. The average would decrease. Cannot be answered without doing calculations.
The average would increase.
On January 28, 1986, the Space Shuttle Challenger broke apart 73 seconds into its flight, killing all seven astronauts on board. All investigations into reasons for the disaster pointed towards the failure of an O-ring in the rocket's engine. Given below is a dotplot and some descriptive statistics on O-ring temperature (°F) for each test firing or actual launch of the shuttle rocket engine.The numeric values of two possible measures of center are calculated to be 65.86°F and 67.50°F. Which one of these is the mean and which the median? How are you deciding? Since the distribution is skewed to the left, the mean will be to the left of the median; hence, 65.86°F is the mean and 67.50°F is the median. Since the distribution is skewed to the right, the mean will be to the right of the median; hence, 67.50°F is the mean and 65.86°F is the median. Since the distribution is skewed to the right, the mean will be to the right of the median; hence, 65.86°F is the mean and 67.50°F is the median. Since the distribution is skewed to the left, the mean will be to the left of the median; hence, 67.50°F is the mean and 65.86°F is the median.
Since the distribution is skewed to the left, the mean will be to the left of the median; hence, 65.86°F is the mean and 67.50°F is the median.
A report from Pew Research Center in 2015 found that in a sample of 929 cell phone users ages 13 to 17, the respondents sent and received an average of 67 texts per day while the median number of texts the same group sent and received per day was only 30. What do these statistics tell you about the shape of the distribution of number of texts sent and received each day by this group? Since the sample size is quite large, the distribution must be fairly bell-shaped. Since the mean and median are different numbers, the distribution must be bimodal. Since the mean is larger than the median, the distribution has mostly smaller values with a few larger values (e.g., it could be skewed to the right). Since the median is smaller than the mean, the distribution has mostly larger values with a few smaller values (e.g., it could be skewed to the left).
Since the mean is larger than the median, the distribution has mostly smaller values with a few larger values (e.g., it could be skewed to the right).
d) Choose the best conclusion based on the p-value. Since the p-value is less than 0.05 we have strong evidence that the average body temperature for females is equal to 98.6 degrees. Since the p-value is less than 0.05 we have strong evidence that the average body temperature for females is less than 98.6 degrees. Since the p-value is less than 0.05 we have strong evidence that the average body temperature for females is greater than 98.6 degrees. Since the p-value is less than 0.05 we have strong evidence that the average body temperature for females is different than 98.6 degrees.
Since the p-value is less than 0.05 we have strong evidence that the average body temperature for females is different than 98.6 degrees.
(e) Shift the data so its mean is as close to 0 as possible. Using the shifted bootstrap sampling distribution, what is your p-value? Using your p-value, do you come to the same conclusion as you did in part (d)? Since the p-value is less than 0.05, we come to the same conclusion. Since the p-value is less than 0.05, we come to a different conclusion. Since the p-value is greater than 0.05, we come to the same conclusion. Since the p-value is greater than 0.05, we come to a different conclusion.
Since the p-value is less than 0.05, we come to the same conclusion.
Choose the best conclusion based on the p-value. Since the p-value is much greater than 0.05, we have strong evidence that the diameter of the sample of needles is different than 1.65mm. Since the p-value is much greater than 0.05, we have strong evidence that the average diameter of the sample of needles is different than 1.65mm. Since the p-value is much greater than 0.05, we do not have strong evidence that the diameter of the population of needles is different than 1.65mm. Since the p-value is much greater than 0.05, we do not have strong evidence that the average diameter of the population of needles is different than 1.65mm.
Since the p-value is much greater than 0.05, we do not have strong evidence that the average diameter of the population of needles is different than 1.65mm.
(c) What is your conclusion about the hypotheses, based on the calculated value of the standardized statistic? How are you deciding?
Since the standardized statistic is less than 2 do not have strong evidence that the average time Cal Poly students watch TV different than 2.84 hours.
In order to estimate the typical amount of TV watched per day by students at her school of 1,000 students, a student has all of the students in her statistics class (30 students) take a short survey, finding that, on average, students in her statistics class report watching 1.2 hours of television per day. What is the population of interest? Choose the answer from the menu in accordance to the question statementStudents in her statistics classStudents at her school
Students at her school
Identify the sample. Choose the answer from the menu in accordance to the question statement All full-time students at the school.All students in the U.S.The 150 students in the sample.
The 150 students in the sample.
Identify the parameter of interest.Choose the answer from the menu in accordance to the question statement The number of students at the school who study.The average daily study time for all full-time students at the school.The proportion of students at the school who study.The average daily study time for the students in the sample (2.23 hours).
The average daily study time for all full-time students at the school
Identify the statistic.Choose the answer from the menu in accordance to the question statement The proportion of students at the school who study.The number of students at the school who study.The average daily study time for all full-time students at the school.The average daily study time for the students in the sample (2.23 hours).
The average daily study time for the students in the sample (2.23 hours).
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 decrease. The average would increase. Cannot be answered without doing calculations. The average 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 increase.
Needles!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 random sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected. For now, suppose that a "problem" is when the sample average diameter turns out to be statistically significantly different from the target of 1.65 mm. Identify the variable of interest and whether the variable is categorical or quantitative.Choose the answer from the menu in accordance to the question statement The diameter of needles and it is categorical.The number of needles, and it is categorical.The diameter of needles and it is quantitative.The average diameter of needles, and it is quantitative.
The diameter of needles and it is quantitative
In the Sampling Words applet with the Gettysburg Address using the variable short, the horizontal axis of the population represents whether or not a word is short - a categorical variable. When you start taking samples of size 10, do the horizontal axes of the two other graphs also represent whether or not a word is short? If not, what do they represent? Are they all categorical variables?
The graph of the most recent sample represents whether or not a word was short, a categorical variable. However, in the graph of the proportions, the horizontal axis represents the proportion of short words in a sample, a quantitative variable.
In the Sampling Words applet with the Gettysburg Address using the variable short, the horizontal axis of the population represents whether or not a word is short - a categorical variable. When you start taking samples of size 10, do the horizontal axes of the two other graphs also represent whether or not a word is short? If not, what do they represent? Are they all categorical variables? The graph of the most recent sample represents whether or not a word was short, a categorical variable. However, in the graph of the proportions, the horizontal axis represents the proportion of short words in a sample, a quantitative variable. The graph of the most recent sample represents whether or not a word was short, a categorical variable. However, in the graph of the proportions, the horizontal axis represents the proportion of short words in the population, a quantitative variable. The graph of the most recent sample represents the number of short words, a quantitative variable. However, in the graph of the proportions, the horizontal axis represents the proportion of short words in a sample, a quantitative variable. The graph of the most recent sample represents the number of short words, a quantitative variable. However, in the graph of the proportions, the horizontal axis represents the proportion of short words in the population, a quantitative variable.
The graph of the most recent sample represents whether or not a word was short, a categorical variable. However, in the graph of the proportions, the horizontal axis represents the proportion of short words in a sample, a quantitative variable.
n the Sampling Words applet with the Gettysburg Address using the variable length, the numbers on the horizontal axis of the graph for the population distribution represent the length of the words - a quantitative variable. When you start taking samples of size 10, do the numbers on the horizontal axes of the two other graphs also represent the length of the words? If not, what do they represent? Are they all quantitative variables? The horizontal axis of the graph of the most recent sample is the length of the words, but the horizontal axis of the graph of the statistic is the mean length of the words in a sample of 10 words. Both of these are quantitative. The horizontal axis of the graph of the most recent sample is the mean length of the words, but the horizontal axis of the graph of the statistic is the length of the words in a sample of 10 words. Both of these are quantitative. The horizontal axis of the graph of the most recent sample is the length of the words, and the horizontal axis of the graph of the statistic is also the length of the words but for a sample of 10 words. Both of these are quantitative. The horizontal axis of the graph of the most recent sample is the mean length of the words, and the horizontal axis of the graph of the statistic is also the mean length of the words but for a sample of 10 words. Both of these are quantitative.
The horizontal axis of the graph of the most recent sample is the length of the words, but the horizontal axis of the graph of the statistic is the mean length of the words in a sample of 10 words. Both of these are quantitative
The more left skewed a distribution is The closer the mean and median are together. The larger the percentage of data values that are above the mean. The smaller the percentage of data values that are above the mean. The percentage of data values above the mean is roughly the same as the percentage of data values below the mean.
The larger the percentage of data values that are above the mean.
(h) You should have seen that when the median is used, there really isn't much of a change between whether the 20 cups per week is used or the 40 cups per week is used. Why don't things change? Comment on the statistic, the standard deviation of the bootstrap sampling distribution, and the p-value.
The observed median and the SD of the sampling distribution did not change because 40 is just a high number just like the 20 was. Therefore, a very similar sampling distribution will be obtained. Because the observed median and the SD of the sampling distribution did not change much, the p-value will not change much.
Using the information from the previous part, describe the parameter of interest for this research question. Choose the answer from the menu in accordance to the question statement Whether or not a student watched TV yesterday.The proportion (or percentage) of all students that watched at least 10 minutes of TV yesterday.The number of students who watched TV for at least 10 minutes yesterday.
The proportion (or percentage) of all students that watched at least 10 minutes of TV yesterday.
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. Describe in words the parameter of interest.
The proportion of U.S. adults who are unhappy with the verdict.
Television news surveyIn 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. 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 that are viewers of the television program. 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 who are unhappy with the verdict.
In order to estimate the proportion of all likely voters who will likely vote for the incumbent in the upcoming city's mayoral race, a random sample of 267 likely voters is taken, finding that 65% state they will likely vote for the incumbent.The polling agency wishes to test whether there is evidence that more than 50% of likely voters will likely vote for the incumbent. Evaluate the strength of evidence for this hypothesis. To which population, if any, are you comfortable drawing your conclusion? Why? The result generalizes to all U.S. citizens because they came from a random sample. The result does not generalize beyond the sample, because it was not a random sample. The result generalizes to all city voters because they came from a random sample.
The result generalizes to all city voters because they came from a random sample.
When using simulation- or theory-based methods to test hypotheses about a proportion, the process of computing a p-value is: Sometimes different and sometimes the same if the sample is from a process instead of a finite population. Different if the sample is from a process instead of from a finite population. The same if the sample is from a process instead of from a finite population.
The same if the sample is from a process instead of from a finite population.
When developing a bootstrap sampling distribution, we repeatedly take samples that are: Larger than the original sample. The same size as the original sample. Smaller than the original sample size. It does not matter. Just take lots of samples.
The same size as the original sample.
In order to investigate how many hours a day full-time students at their school tend to spend on course work outside of regularly scheduled class time, a statistics student takes a random sample of 150 students from their school by randomly choosing names from a list of all full-time students at their school that semester. The student finds that the average reported daily study hours among the 150 students is 2.23 hours. Explain whether or not you believe the sample is representative of the population of interest and why.
The sample is random, so the sample should be representative of the population of interest.
For a given population of a single quantitative variable, by what factor must the sample size increase in order for the standard deviation of the sampling distribution of the mean to be half as large? The sample size must be two times as large. The sample size must be four times as large. There is not enough information to answer.
The sample size must be four times as large.
A zoologist at a large metropolitan zoo is concerned about a potential new disease present among the 243 sharks living in the large aquarium at the zoo. The zoologist takes a random sample of 15 sharks from the aquarium, temporarily removes the sharks from the tank, and tests them for the disease. He finds that 3 of the sharks have the disease.The zoologist wishes to test whether there is evidence that less than one-fourth of the sharks in the aquarium are diseased. Evaluate the strength of evidence for this hypothesis. Find the p-value for the hypothesis using a simulation-based approach. In which population, if any, are you comfortable drawing your conclusion?
The sharks at the zoo
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 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? Cannot be answered without doing calculations. The standard deviation would decrease. The standard deviation would increase. The standard deviation would stay the same.
The standard deviation 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 standard deviation of the three salaries change?
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 increase. The standard deviation would stay the same. The standard deviation would decrease.
The standard deviation would stay the same.
A t-distribution looks a lot like a normal distribution, but it is a bit more spread out than a normal distribution with more observations in the "tails," fewer in the middle. To determine whether a result is out in the tail of a normal distribution, we use a standardized statistic of 2 as our guideline. We can use the same guideline for t-distributions. Suppose, however, the standardized statistic of 2 was a precise rule for a normal distribution. Would the corresponding precise rule for a t-distribution use a number that was more or less than 2?
The standardized statistic should be more than 2 because a t-distribution has more area (probability) in the tail, we would have to move the standardized statistic out farther to reduce the probability to what you would find beyond 2 in the tail of a normal distribution.
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 appropriate because there are at least 10 successes and 10 failures in the data, p = 0.0001.
A zoologist at a large metropolitan zoo is concerned about a potential new disease present among the 243 sharks living in the large aquarium at the zoo. The zoologist takes a random sample of 15 sharks from the aquarium, temporarily removes the sharks from the tank, and tests them for the disease. He finds that 3 of the sharks have the disease.The zoologist wishes to test whether there is evidence that less than one-fourth of the sharks in the aquarium are diseased. Evaluate the strength of evidence for this hypothesis. 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 diseased sharks.
There is no evidence that the proportion of diseased sharks in the zoo is less than 0.25
In order to estimate the proportion of all likely voters who will likely vote for the incumbent in the upcoming city's mayoral race, a random sample of 267 likely voters is taken, finding that 65% state they will likely vote for the incumbent.The polling agency wishes to test whether there is evidence that more than 50% of likely voters will likely vote for the incumbent. Evaluate the strength of evidence for this hypothesis. 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 likely voting outcome in the mayoral race if the election were to take place today. There is no evidence that a majority of city voters will vote for the incumbent. There is weak evidence that a majority of city voters will vote for the incumbent. There is strong evidence that a majority of city voters will vote for the incumbent.
There is strong evidence that a majority of city voters will vote for the incumbent.
In order to estimate the typical amount of TV watched per day by students at her school of 1,000 students, a student has all of the students in her statistics class (30 students) take a short survey. In the survey the student asked students whether or not they watched at least 10 minutes of TV yesterday. The student found that 21 of 30 students reported watching at least 10 minutes of TV yesterday. The student wishes to test whether there is evidence that more than 50% of students at the school watched at least 10 minutes of TV yesterday. Evaluate the strength of evidence for this hypothesis. Calculating the p-value for the hypothesis using a simulation-based approach gives a p-value of 0.0214. Based on the p-value evaluate the strength of evidence and state a conclusion about the TV watching among students yesterday. Choose the answer from the menu in accordance to the question statement
There is strong evidence that students watched more than 10 minutes of TV yesterday.
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.
There is strong evidence that the proportion of US adults who opposed to the verdict is greater than .75
What is the primary reason why we create a bootstrap sampling distribution? To see where the distribution is centered. To see what shape the distribution will have. To see how the means or medians vary by finding the SD of the sampling distribution. All of the above.
To see how the means or medians vary by finding the SD of the sampling distribution.
Larger random samples are always better than smaller random samples.
True
You should not take a random sample of more than 5% of the population size.
True
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?
Type 1 error is possible here
When surveys are administered, it is hoped that the respondents give accurate answers. Does the mode of survey delivery affect this? American researchers investigated this question (Schober et al., 2015). They had 634 people agree to be interviewed on an iPhone and they were randomly assigned to receive a text message or a phone call. One question that was asked was whether they exercise less than once per week on a typical week (an example of a question in which an answer of "yes" would be considered socially undesirable). They found that 25.4% of those that received text messages responded yes, while only 13.2% of those that received phone calls responded yes. This difference is statistically significant, and one could assume that one method of the delivery of the question is biased. Which of these results do you think are the result of a biased method of collecting the data and why? Choose the best among the following statements.
Using a phone call as the method of asking this question is probably a biased method. Those answering a person on a phone call were much more unlikely to say that they exercise less than once per week. Having an interaction with a person probably makes some people not give the socially undesirable answer.
In order to estimate the proportion of all likely voters who will likely vote for the incumbent in the upcoming city's mayoral race, a random sample of 267 likely voters is taken, finding that 65% state they will likely vote for the incumbent.The polling agency wishes to test whether there is evidence that more than 50% of likely voters will likely vote for the incumbent. Evaluate the strength of evidence for this hypothesis. If a theory-based approach would be reasonable for these data, find the p-value and comment on the similarity of the p-value from the theory-based approach to the p-value you found in (a). If a theory-based approach would not be reasonable for these data, explain why not. Using theory-based methods is appropriate, and the obtained p-value is close to 1. Using theory-based methods is not appropriate, as the obtained p-value is different. Using theory-based methods is appropriate, and the obtained p-value is approximately 0. Using theory-based methods is not appropriate, as the sample size is too small.
Using theory-based methods is appropriate, and the obtained p-value is approximately 0.
In order to understand more about how people in the United States feel about the outcome of a recent criminal trial in which the defendant was found not guilty, a television news program invites viewers to go the news programs 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 survey also asked participants to report the time the respondent spent reading or watching news coverage about the trial during the past three days. The poll found that, on average, respondents had spent 92 minutes reading or watching news coverage about the trial during the past three days. Identify the variable measured on each respondent.
Variable is time spent reading/watching news coverage
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.
Whether someone is unhappy with the verdict
When developing a bootstrap sampling distribution, we repeatedly take random samples:
With replacement from the original sample.
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.
buzz is guessing but we determine that he is not guessing
What do you expect the means and standard deviations of the distribution of sample means to be when the samples are drawn from a large population with the following parameters and sample sizes? Round answer to 1 decimal place, e.g. 0.7. (a) μ=10, σ=4, n=25
mean=10 SD=.8
On January 28, 1986, the Space Shuttle Challenger broke apart 73 seconds into its flight, killing all seven astronauts on board. All investigations into reasons for the disaster pointed towards the failure of an O-ring in the rocket's engine. Given below is a dotplot and some descriptive statistics on O-ring temperature (°F) for each test firing or actual launch of the shuttle rocket engine.If we removed the observation 31°F from the data set, how would the following numerical statistics change, if at all?
mean=larger, median=larger, std dev=smaller
Suppose that the most recent random sample of 35 needles have an average diameter of 1.64 mm and a standard deviation of 0.07 mm. Assign appropriate symbols to these numbers.Choose the answer from the menu in accordance to the question statement n = 35, µ = 1.64, σ = 0.07n = 35, x-bar = 1.64, σ = 0.07n = 35, x-bar = 1.64, s = 0.07n = 35, µ = 1.64, s = 0.07
n = 35, x-bar = 1.64, σ = 0.07
Suppose that the most recent random sample of 35 needles have an average diameter of 1.64 mm and a standard deviation of 0.07 mm. Assign appropriate symbols to these numbers.
n=35 xbar=1.64 sd=.07
Is the variable categorical or quantitative? Choose the answer from the menu in accordance to the question statement
quantitative
Reconsider Dr. Sameer's research question about how much time Cal Poly students spend on watching television. Suppose that for the random sample of 100 Cal Poly students the mean number of hours per day spent watching TV turns out to be 3.01 hours, and the standard deviation of the number of hours per day spent watching TV turns out to be 1.97 hours. (a) Is the number 1.97 a parameter or a statistic? Assign an appropriate symbol to this number.
s=1.97 is a statistic.
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 random sample of several needles and measure their diameters. If they discover a problem, they will stop the manufacturing process until it is corrected. For now, suppose that a "problem" is when the sample average diameter turns out to be statistically significantly different from the target of 1.65 mm. Suppose that the most recent random sample of 35 needles have an average diameter of 1.64 mm and a standard deviation of 0.07 mm. Use the Theory-Based Inference applet to find and report a standardized statistic (t-statistic) and a p-value to investigate whether the average diameter of needles produced by this manufacturing process is different from 1.65 mm. Report answers as provided in the applet (no rounding). t-statistic = and p-value =
t=-0.85, p=0.4039
(c) The sample mean body temperature for the 65 females in our sample is 98.39°F and the standard deviation is 0.743°F. Use the Theory-Based Inference applet to find and report a standardized statistic (t-statistic) and a p-value for the test. Report answers as provided in the applet (no rounding). t-statistic = and p-value =
t=-2.28, p=0.0260
(b) Click on the One Mean applet, choose the Bootstrapping option at the top, and paste in the data. What are the mean and standard deviation for the morphing data?
xbar=6.292, s=12.449
Which of the following is correct? x¯ and s represent statistics while μ and σ represent parameters. x¯ and μ represent statistics while s and σ represent parameters. s and σ represent statistics while x¯ and μ represent parameters. μ and σ represent statistics while x¯ and s represent parameters.
x¯ and s represent statistics while μ and σ represent parameters.
b) Click on the One Mean applet, choose the Bootstrapping option at the top, and paste in the data. What are the mean and standard deviation for the morphing data? x¯=6.296, s=12.449 μ=6.296, σ=12.449 x¯=12.449, s=6.296 μ=12.449, σ=6.296
x¯=6.296, s=12.449