Stats Exam 1

In 2015 there was a viral story about the colors of a dress in a picture. Some saw the colors as blue and black and others saw them as white and gold. Suppose you take a sample of 100 people and ask them which of the two color combinations they think the dress is. You want to see whether a majority think that the dress is blue and black (the actual colors of the dress). Also suppose you find that 57 out of your sample of 100 correctly identified the colors as blue and black. To conduct a simulation analysis of this study, you could flip a coin ______ times and repeat that process at least 1,000 times. (The answer is coded wrong here. The correct answer should be 100.) Select one: A. 1,000 B. 1 C. 57 D. 100

D

Suppose we obtain a p-value of 0.2020, we can say we have: Select one: A. Strong evidence for the null hypothesis. B. Moderate evidence against the null hypothesis, but not strong. C. Strong evidence against the null hypothesis. D. Both little to no evidence against the null hypothesis and strong evidence for the null hypothesis. E. Little to no evidence against the null hypothesis.

E

Suppose a 95% confidence interval is constructed from a sample proportion and 0.50 is contained in the interval. Which of the following is true? Select one: A. A 99% confidence interval constructed from the same sample proportion will definitely contain 0.50. B. A 90% confidence interval constructed from the same sample proportion will definitely contain 0.50. C. A 99% confidence interval constructed from the same sample proportion will definitely NOT contain 0.50. D. A 90% confidence interval constructed from the same sample proportion will definitely NOT contain 0.50.

a

Suppose a friend of yours says she is a 75% free-throw shooter in basketball. You don't think she is that good and want to test her to gather evidence that she makes less than 75% of her free throws in the long run. You have her shoot 30 free throws and she makes 18 (or 60%) of them. Are the validity conditions met for the one-proportion z-test? Select one: A. Yes, because the number of success and failures are each at least 10. B. No, because the number of success and failures are each at least 10. C. No, because the sample size is less than 40. D. Yes, because the sample size is more than 20.

a

The Gettysburg address has 268 words and 41.0% of the words are short (3 or fewer letters). If we are going to randomly choose words from that speech, which of the following is least likely to happen? Select one: A. Randomly picking 10 words from the Gettysburg Address and have all of them be short. B. Randomly picking a word from the Gettysburg Address and have it be short. C. Randomly picking 5 words from the Gettysburg Address and have all of them be short.

a

The p-value of a test of significance is: Select one: A. The probability, assuming the null hypothesis is true, that we would get a result at least as extreme as the one that was actually observed B. The probability, assuming the alternative hypothesis is true, that we would get a result at least as extreme as the one that was actually observed C. The probability the alternative hypothesis is true D. The probability the null hypothesis is true

a

The theorem that states that if the sample size is large enough, the distribution of sample proportions will be bell-shaped (approximately normal), centered at the long run proportion π, with a standard deviation of square root of (pi(1-pi))/n is called: Select one: A. The central limit theorem. B. The theory-based theorem. C. The normal theorem. D. The fundamental theorem of statistics.

a

A t-distribution is shaped like a normal distribution but is: Select one: A. Not quite as spread out with fewer observations in the tails than a normal distribution. B. A bit more spread out and more observations in the tails than a normal distribution. C. A bit taller in the middle than a normal distribution. D. A bit skewed in one direction or the other.

b

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? Select one: A. Randomly picking a word from the Gettysburg Address and have it be 2 or fewer letters in length. B. Randomly picking 10 words from the Gettysburg Address and have the mean be 2 or fewer letters in length. C. Randomly picking 5 words from the Gettysburg Address and have the mean be 2 or fewer letters in length.

b

The more right skewed a distribution is Select one: A. The percentage of data values below the mean is roughly the same as the percentage of data values above the mean B. The larger the percentage of data values that are below the mean C. The closer the mean and median are D. The smaller the percentage of data values that are below the mean

b

LeBron James of the Los Angeles Lakers hit 558 of his 1,095 field goal attempts in the 2018/2019 season for a shooting percentage of 51.0%. 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 2018/2019 season under the assumption of the chance model. a. Flip a coin 1,095 times and record the number of heads. This number represents the long-run proportion. b. Flip a coin 558 times and record the number of heads. Multiply this value by 1,095. c. Flip a coin 1,095 times and record the number of heads. Repeat this 1,000 times, keeping track of the number of heads in each set of 1,095. d. Flip a coin 1,000 times and record the number of heads. Repeat this process 558 times.

c

LeBron James of the Los Angeles Lakers hit 558 of his 1,095 field goal attempts in the 2018/2019 season for a shooting percentage of 51.0%. 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 51.0%? sample chance model statistic parameter

c

LeBron James of the Los Angeles Lakers hit 558 of his 1,095 field goal attempts in the 2018/2019 season for a shooting percentage of 51.0%. Over the lifetime of LeBron's career, can we say he is more likely than not to make a field goal?​ a. Describe the parameter of interest. a. the number of shots LeBron made in the 2018/2019 season b. the proportion of all shots made by NBA players in LeBron's career c. LeBron's long-run proportion of making a field goal d. the proportion of shots LeBron made in the 2018/2019 season

c

Let π denote some population proportion of interest and suppose a 95% confidence interval for π is calculated to be (0.63, 0.73) and a 99% confidence interval for π is calculated to be (0.61, 0.75). Also, suppose that we want to test H0: π = 0.74 vs. Ha: π ≠ 0.74 What can you say about the corresponding p-value? Select one: A. I can't say anything about the corresponding p-value until I run the test. B. The corresponding p-value will be larger than 0.05. C. The corresponding p-value will be smaller than 0.05 but larger than 0.01. D. The corresponding p-value will be smaller than 0.01.

c

LeBron James of the Los Angeles Lakers hit 558 of his 1,095 field goal attempts in the 2018/2019 season for a shooting percentage of 51.0%. 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 2018/2019 season under the assumption of the chance model. What would be a typical number of heads recorded from a repetition of 1,095 coin flips? a. 51.0% of 1,095 (558) will be one of the most likely values since we assume the chance model is true and the chance probability is 51.0%. b. Approximately ½ of 1,095 (547) will be one of the most likely values since we assume the chance model is true. c. LeBron James is a great player so we can assume he will make at least 60% of his shots. d. Nothing can be known about the typical number of heads without doing the simulation.

B

Suppose you are conducting a test of significance to try to determine whether your cat, Hope, will go to the correct object (out of two) when it is pointed to, just like Harley the dog did in the Exploration 1.1. You test Hope 100 times and finds she goes to the correct object in 70 of those 100 trials. In this scenario, what are the observational units? Select one: A. The long-term proportion (probability) that Hope will go to the correct object. B. The 100 trials. C. The proportion of the 100 trials that Hope goes to the correct object. D. Whether or not Hope goes to the correct object.

B

Suppose you are conducting a test of significance to try to determine whether your cat, Hope, will go to the correct object (out of two) when it is pointed to, just like Harley the dog did in the Exploration 1.1. You test Hope 100 times and finds she goes to the correct object in 70 of those 100 trials. In this scenario, what is the parameter? Select one: A. The 100 trials. B. The long-term proportion (probability) that Hope will go to the correct object. C. The proportion of the 100 trials that Hope goes to the correct object. D. Whether or not Hope goes to the correct object.

B

Suppose you are conducting a test of significance to try to determine whether your cat, Hope, will go to the correct object (out of two) when it is pointed to, just like Harley the dog did in the Exploration 1.1. You test Hope 100 times and finds she goes to the correct object in 70 of those 100 trials. In this scenario, what is the variable? Select one: A. The 100 trials. B. Whether or not Hope goes to the correct object. C. The proportion of the 100 trials that Hope goes to the correct object. D. The long-term proportion (probability) that Hope will go to the correct object.

B

Suppose you are using theory-based techniques (e.g., a one-proportion z-test) to determine p-values. How will a two-sided p-value compare to a one-sided p-value (assuming the one-sided p-value is less than 0.50)? Select one: A. The two-sided p-value will be close to twice as large as the one-sided. B. The two-sided p-value will be exactly twice as large as the one-sided. C. The two-sided p-value will be about the same as the one-sided. D. The two-sided p-value will be half as much as the one-sided.

B

Which of the following is the most important reason that a simulation analysis would repeat the coin-flipping process many times? Select one: A. To see whether the distribution of sample proportions follows a normal, bell-shaped curve B. To see how much variability results in the distribution of sample proportions C. To see whether the distribution of sample proportions is centered at 0.50

B

Suppose you are conducting a test of significance to try to determine whether your cat, Hope, will go to the correct object (out of two) when it is pointed to, just like Harley the dog did in the Exploration 1.1. You test Hope 100 times and finds she goes to the correct object in 70 of those 100 trials. In this scenario, what is the statistic? Select one: A. The proportion of the 100 trials that Hope goes to the correct object. B. Whether or not Hope goes to the correct object. C. The 100 trials. D. The long-term proportion (probability) that Hope will go to the correct object

A

Although we know some animals, like dogs, have a keen sense of smell, what about humans? A woman from Scotland, Joy Milne, claimed that she was able to determine whether or not someone had Parkinson's disease just based on their smell (Morgan, J., 2016). Her husband died from the disease and she noticed that he started smelling different prior to his diagnosis. To test this, researchers had six people known to have Parkinson's disease and six people thought not to have the disease wear t-shirts for a day. They collected the shirts and then tested Milne. She correctly identified 11 of the 12 shirts. Set up the correct null and alternative hypotheses in symbols to test this scenario.

Ho= pi=50 Ha= pi > 50

Suppose I am conducting a test of significance where the null hypothesis is my cat Cayle will pick the correct cancer specimen 25% of the time and the alternative hypothesis is that she will pick the cancer specimen at a rate different than 25%. I end up with a p-value of 0.002. I also construct 95% and 99% confidence intervals from my data. What will be true about my confidence intervals? Select one: A. Neither the 95% nor the 99% intervals will contain 0.25. B. The 95% interval will not contain 0.25, but the 99% interval will contain 0.25. C. Both the 95% and the 99% intervals will contain 0.25. D. The 95% interval will contain 0.25, but the 99% interval will not contain 0.25.

a

Suppose a 95% confidence interval for a population proportion is found using the 2SD or theory-based method. Which of the following will definitely be contained in that interval? Select one: A. The sample proportion B. The population proportion C. All of the above D. The p-value

a

According to the 2019 National Coffee Drinking Study from the National Coffee Association, 63% of 2,815 U.S. adults respondents reported drinking coffee in the past 24 hours. Based on these data, a theory-based 99% confidence interval for the proportion of all adult Americans that drank coffee in the previous 24 hours is: Select one: A. 0.6064 to 0.6533 B. 0.6120 to 0.6477 C. 0.5930 to 0.6670 D. 0.6149 to 0.6448

a

Based on 7 of the last 10 slices of toast landing buttered side down and the dotplot, would you be convinced that the long-run proportion of times my toast lands buttered side down is greater than 50%, and why? a. No, 7 is a fairly typical outcome assuming the parameter is 50%. b. No, 7 is a fairly typical outcome assuming the parameter is 70%. c. Yes, 7 is a fairly typical outcome assuming the parameter is 70%. d. Yes, 7 is a fairly typical outcome assuming the parameter is 50%.

a

Based on the dotplot, does this prove that my long-run proportion of dropping toast buttered side down is 50%? a. No, 50% is just a plausible value of the parameter. b. Yes, statistical analyses prove that results are true. c. No, this proves that the parameter is 70%. d. Yes, 50% is the most typical value.

a

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? Select one: A. 0.50 B. 7.12 C. 1.59 D. 0.10 E. 2.25

a

If you are testing the hypotheses H0: π = 0.60 and Ha: π ≠ 0.60, have a sample proportion of 0.75 and get a p-value of 0.021, what can you say about a 99% confidence interval constructed using the same data? Select one: A. The 99% confidence interval will definitely contain 0.60. B. The 99% confidence interval will definitely not contain 0.60. C. The 99% confidence interval will definitely contain 0.021. D. None of the above. E. The 99% confidence interval will definitely not contain 0.75.

a

In Example 1.1, we looked at a study to investigate whether dolphins could communicate the idea of left and right. In doing so, we tested whether Buzz, one of the dolphins, understands the communication so would push the correct button more than 50% of the time in the long run. Describe what a Type I error (rejecting a true null hypothesis) would be in this study. a. Buzz does NOT understand the communication so is guessing, but we have strong evidence that he understands the communication b. Buzz understands the communication, but we do NOT have strong evidence that he understands

a

LeBron James of the Los Angeles Lakers hit 558 of his 1,095 field goal attempts in the 2018/2019 season for a shooting percentage of 51.0%. 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? 0.50 0.565 558 0.25

a

Let π denote some population proportion of interest and suppose a 99% confidence interval for π is calculated to be (0.60, 0.70). Also, suppose that we want to test H0: π = 0.74 vs. Ha : π ≠ 0.74 What can you say about the corresponding p-value? Select one: A. The corresponding p-value will be smaller than 0.01. B. The corresponding p-value will be smaller than 0.05 but larger than 0.01. C. The corresponding p-value will be larger than 0.05. D. I can't say anything about the corresponding p-value until I run the test.

a

Spam filters in an email program are similar to hypothesis tests in that there are two possible decisions and two possible realities and therefore two kinds of errors that can be made. The hypotheses can be considered as: H0: Incoming email message is legitimate. Ha: Incoming email message is spam. Describe what rejecting a true null hypothesis means in this context. (This is also known as a Type I error.) a. The message is legitimate, but you have strong evidence that the message is spam. b. The message is spam, but you do not have strong evidence that the message is spam. c. The message is spam, but you have strong evidence that the message is legitimate.

a

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? Select one: A. 10 B. 0.40 C. 0.50 D. 0.60

b

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 pictures of each subject's face morphed with that of someone who 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 also 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. Put the data, in the file Morphing, into the Theory-Based Inference applet to answer the following. Construct a 95% confidence interval for the average score for some population of people doing this activity. a. (-1.37, 11.22) b. (1.37,11.22) c. (-11.22, -1.37) d. (-11.22, 1.37)

b

In Example 1.1, we looked at a study to investigate whether dolphins could communicate the idea of left and right. In doing so, we tested whether Buzz, one of the dolphins, understands the communication so would push the correct button more than 50% of the time in the long run. Describe what a Type II error (not rejecting a false null hypothesis) would be in this study. a. Buzz does NOT understand the communication so is guessing, but we have strong evidence that he understands the communication b. Buzz understands the communication, but we do NOT have strong evidence that he understands

b

Let π denote some population proportion of interest and suppose a 95% confidence interval for π is calculated to be (0.60, 0.70). Also, suppose that we want to test H0 : π = 0.63 vs. Ha : π ≠ 0.63. What can you say about the corresponding p-value? Select one: A. Need more information to answer this. B. The corresponding p-value will be larger than 0.05. C. The corresponding p-value will be smaller than 0.05.

b

Normal (or average) body temperature of humans is often thought to be 98.6°F. Is that number really the average body temperature for human females? To test this, we will use a data set which consists of 65 body temperatures from healthy female volunteers aged 18 to 40 that were participating in 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? a. H0: μ = 98.6°F and Ha: μ < 98.6°F b. H0: μ = 98.6°F and Ha: μ ≠ 98.6°F c. H0: x̄ = 98.6°F and Ha: x̄ < 98.6°F d. H0: x̄ = 98.6°F and Ha: x̄ ≠ 98.6°F

b

Spam filters in an email program are similar to hypothesis tests in that there are two possible decisions and two possible realities and therefore two kinds of errors that can be made. The hypotheses can be considered as: H0: Incoming email message is legitimate. Ha: Incoming email message is spam. Describe what failing to reject H0 means in this context. a. Having strong evidence that the incoming email message is spam b. Not having strong evidence that the incoming email message is spam c. Having strong evidence that the incoming email message is legitimate

b

Spam filters in an email program are similar to hypothesis tests in that there are two possible decisions and two possible realities and therefore two kinds of errors that can be made. The hypotheses can be considered as: H0: Incoming email message is legitimate. Ha: Incoming email message is spam. Describe what failing to reject a false null hypothesis error means in this context. (This is also known as a Type II error.) a. The message is legitimate, but you have strong evidence that the message is spam. b. The message is spam, but you do not have strong evidence that the message is spam. c. The message is spam, but you have strong evidence that the message is legitimate.

b

Suppose 10 coins are flipped, and the proportion of heads is recorded. This process is repeated many, many times to develop a distribution of these sample proportions. What is the predicted mean and standard deviation for this distribution of sample proportions? Select one: A. Mean = 5.000, SD = 1.581 B. Mean = 0.500, SD = 0.158 C. Mean = 5.000, SD = 0.581 D. Mean = 0.500, SD = 1.581

b

Suppose I am conducting a test of significance where the null hypothesis is my cat Cayce will pick the correct cancer specimen 25% of the time and the alternative hypothesis is that he will pick the cancer specimen at a rate different than 25%. I end up with a p-value of 0.07. I also construct 95% and 99% confidence intervals from my data. What will be true about my confidence intervals? Select one: A. Neither the 95% nor the 99% intervals will contain 0.25. B. Both the 95% and the 99% intervals will contain 0.25. C. The 95% interval will not contain 0.25, but the 99% interval will contain 0.25. D. The 95% interval will contain 0.25, but the 99% interval will not contain 0.25.

b

Suppose I am conducting a test of significance where the null hypothesis is my cat Grayce will pick the correct cancer specimen 25% of the time and the alternative hypothesis is that she will pick the cancer specimen at a rate different than 25%. I end up with a p-value of 0.02. I also construct 95% and 99% confidence intervals from my data. What will be true about my confidence intervals? Select one: A. Neither the 95% nor the 99% intervals will contain 0.25. B. The 95% interval will not contain 0.25, but the 99% interval will contain 0.25. C. Both the 95% and the 99% intervals will contain 0.25. D. The 95% interval will contain 0.25, but the 99% interval will not contain 0.25.

b

Suppose that birth weights of babies in the U.S. have a mean of 3,250 grams and standard deviation of 550 grams. Based on this information, which of the following is more unlikely? Choose one. Select one: A. A randomly selected baby has a birth weight greater than 4,000 grams. B. A random sample of 10 babies has an average birth weight greater than 4,000 grams. C. Both are equally likely. D. Cannot be answered without doing calculations.

b

Suppose we have a list of all 3,000 students in your college and we randomly choose 30 from that list. Each of these 30 people is sent a survey and 25 are returned. In this scenario, what is the sampling frame? Select one: A. The 25 people that returned the survey B. The list of all 3,000 people in your college C. The 30 people sent the survey D. The mechanism used to randomly choose the 30 students E. The survey

b

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. Select one: A. Both methods of asking this question are probably biased. It is expected about 50% of participants to answer "yes", but both methods led to values much smaller than 50%. B. 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. C. Using the text message as the method of asking this question is probably a biased method. The percentage of participants saying "yes" who received text messages is almost twice the percentage of participants saying "yes" who received a phone call. Text message participants are much more likely to say they exercise less. D. None of the methods of asking this question are biased. The difference could be just due to chance.

b

Although we know some animals, like dogs, have a keen sense of smell, what about humans? A woman from Scotland, Joy Milne, claimed that she was able to determine whether or not someone had Parkinson's disease just based on their smell (Morgan, J., 2016). Her husband died from the disease and she noticed that he started smelling different prior to his diagnosis. To test this, researchers had six people known to have Parkinson's disease and six people thought not to have the disease wear t-shirts for a day. They collected the shirts and then tested Milne. She correctly identified 11 of the 12 shirts. a. Let π represent the probability that Joy Milne can correctly determine whether someone has Parkinson's disease from smelling their shirt. What is the value of π if she is just guessing? a. 0.92 b. 0.25 c. 0.50 d. 0.05

c

Based on a June 2019 Gallup poll, a 95% confidence interval for the proportion of American adults that think a college education is very important is 0.50 to 0.56. Explain exactly what the confidence interval is estimating. Select one: A. The number of American adults in the sample that think a college education is very important. B. The proportion of American adults in the poll that think a college education is very important. C. The proportion of all American adults that think a college education is very important. D. Whether 0.50 to 0.56 of American adults think a college education is very important.

c

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: Select one: A. Take fewer samples. B. Take more samples. C. Used a larger sample size. D. Used a smaller sample size.

c

Milne was adamant that one of the shirts came from someone with the disease when, in fact, that person had not been diagnosed. However, eight months later, the person she claimed had Parkinson's was given a diagnosis that he had the disease. So she, in fact, got all 12 correct! Using this new statistic of 12 out of 12, determine the standardized statistic for the observed sample proportion of "successes." Does this now give stronger or weaker evidence that she is doing better than just guessing than if she only got 11 out of 12 correct like what was originally thought? a. Stronger evidence, because the standardized statistic is around 6.2 which is farther from 0 than the previous standardized statistic. b. Weaker evidence, because the standardized statistic is around 3.5 which is farther from 0 than the previous standardized statistic. c. Stronger evidence, because the standardized statistic is around 3.5 which is farther from 0 than the previous standardized statistic. d. Weaker evidence, because the standardized statistic is around 6.2 which is farther from 0 than the previous standardized statistic.

c

Normal (or average) body temperature of humans is often thought to be 98.6°F. Is that number really the average body temperature for human males? To test this, we will use a data set which consists of 65 body temperatures from healthy male volunteers aged 18 to 40 that were participating in vaccine trials. The data set is also available from the textbook website and is names MaleTemps. What are the appropriate null and alternative hypotheses for this study? a. H0: The average body temperature for males is 98.6°F and Ha: The average body temperature for males is greater than 98.6°F b. H0: The average body temperature for males is 98.6°F and Ha: The average body temperature for males is smaller than 98.6°F c. H0: The average body temperature for males is 98.6°F and Ha: The average body temperature for males is not 98.6°F

c

Spam filters in an email program are similar to hypothesis tests in that there are two possible decisions and two possible realities and therefore two kinds of errors that can be made. The hypotheses can be considered as: H0: Incoming email message is legitimate. Ha: Incoming email message is spam. Describe what rejecting H0 means in this context. a. Having strong evidence that the incoming email message is spam b. Not having strong evidence that the incoming email message is spam c. Having strong evidence that the incoming email message is legitimate

c

Suppose a friend of yours says she is a 75% free-throw shooter in basketball. You don't think she is that good and want to test her to gather evidence that she makes less than 75% of her free throws in the long run. You have her shoot 40 free throws and she makes 26 (or 65%) of them. Which of the following is an appropriate way to set up the hypotheses, in symbols, for this test? Select one: A. H0: p̂ = 0.65, Ha: p̂ < 0.65 B. H0: p̂ = 0.75, Ha: p̂ < 0.75 C. H0: π = 0.75, Ha: π < 0.75 D. H0: π = 0.65, Ha: π < 0.65 E. H0: π < 0.75, Ha: π = 0.75

c

Suppose a friend of yours says she is a 75% free-throw shooter in basketball. You don't think she is that good and want to test her to gather evidence that she makes less than 75% of her free throws in the long run. You have her shoot 40 free throws and she makes 26 (or 65%) of them. Which of the following is the appropriate sample statistic and proper symbol? Select one: A. n = 26 B. p̂ = 0.75 C. p̂ = 0.65 D. π = 0.75 E. π = 0.65

c

Suppose that a standardized statistic (standardized sample proportion) for a study is calculated to be 2.45. Which of the following is the most appropriate interpretation of this standardized statistic? Select one: A. The study results are statistically significant B. The observed value of the sample proportion is 2.45 SDs away from the hypothesized parameter value. C. The observed value of the sample proportion is 2.45 SDs above the hypothesized parameter value. D. The observed value of the sample proportion is 2.45 times the hypothesized parameter value.

c

Suppose the distribution of the length of the words in a chapter of your textbook has a mean of 5 words and a standard deviation 2.7 words. Also suppose I take repeated samples of 10 words from all the words in the chapter, calculate the mean of each sample, and repeat this 1,000 times. What will be true about the resulting distribution of sample mean word lengths? Select one: A. The distribution will have a mean of about 5 words and a standard deviation greater than 2.7 words. B. The distribution will have a mean of about 5 words and a standard deviation of about 2.7 words. C. The distribution will have a mean of about 5 words and a standard deviation less than 2.7 words. D. Since this samples were randomly taken, we have no way to predict the values of the resulting mean and standard deviation.

c

The more left skewed a distribution is Select one: A. The smaller the percentage of data values that are above the mean B. The closer the mean and median are together C. The larger the percentage of data values that are above the mean D. The percentage of data values above the mean is roughly the same as the percentage of data values below the mean

c

What does each dot represent in terms of dropped toast and buttered side down? a. the number of "buttered side down" attempts in 100 flips of the toast b. the number of times out of 10 attempts the toast lands buttered side down when the probability that the toast lands buttered side down is 70% c. the number of times out of 10 attempts the toast lands buttered side down when the probability that the toast lands buttered side down is 50% d. the number of times more than 5 "buttered side down" results out of 10 occurred

c

When we get a p-value that is very large, we may conclude that: Select one: A. There is strong evidence for the alternative hypothesis. B. The null hypothesis has been proven to be true. C. The null hypothesis is plausible. D. The alternative hypothesis has been proven to be false.

c

Which sample size, n, gives the smallest standard deviation of the null distribution where the long-run proportion, π, is 0.25? Select one: A. 30 B. 50 C. 60 D. 40

c

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 pictures of each subject's face morphed with that of someone who 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 also 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. Put the data, in the file Morphing, into the Theory-Based Inference applet to answer the following. Based on your confidence interval, do you have strong evidence that, on average, people tend to pick a face that is more attractive than their own when they are asked to identify their own face? a. Yes, we have strong evidence that, on average, people tend to pick a face that is more attractive than their own when they are asked to identify their own face because the 95% confidence interval for the average score only has negative numbers. b. No, we do not have strong evidence that, on average, people tend to pick a face that is more attractive than their own when they are asked to identify their own face because the 95% confidence interval for the average score includes both positive and negative numbers. c. No, we do not have strong evidence that, on average, people tend to pick a face that is more attractive than their own when they are asked to identify their own face because it is not possible to answer this question just based on the confidence interval. d. Yes, we have strong evidence that, on average, people tend to pick a face that is more attractive than their own when they are asked to identify their own face because the 95% confidence interval for the average score only has positive numbers.

d

If you are testing the hypotheses H0: π = 0.50 and Ha: π ≠ 0.50, have a sample proportion of 0.60 and get a p-value of 0.321, what can you say about a 95% confidence interval constructed using the same data? Select one: A. The 95% confidence interval will definitely not contain 0.321. B. The 95% confidence interval will definitely not contain 0.50. C. The 95% confidence interval will definitely not contain 0.60. D. The 95% confidence interval will definitely contain 0.50. E. The 95% confidence interval will definitely contain 0.321.

d

Suppose a friend of yours says she is a 75% free-throw shooter in basketball. You don't think she is that good and want to test her to gather evidence that she makes less than 75% of her free throws in the long run. You have her shoot 40 free throws and she makes 26 (or 65%) of them. You run this test and find a p-value of 0.1150. Which of the following is the best way to state the conclusion? Select one: A. Because the p-value is large, there is strong evidence that your friend is a 75% free-throw shooter in the long run. B. Because the p-value is small, there is strong evidence that your friend is less than a 75% free-throw shooter in the long run. C. Because the p-value is small, there is strong evidence that your friend is a 75% free-throw shooter in the long run. D. Because the p-value is not small enough, there is not strong evidence that your friend is less than a 75% free-throw shooter in the long run. E. Because the p-value is large, there is strong evidence that your friend is a 65% free-throw shooter in the long run.

d

Suppose a researcher is testing to see if a basketball player can make free throws at a rate higher than the NBA average of 75%. The player is tested by shooting 10 free throws and makes 8 of them. In conducting the related test of significance we have a computer applet do an appropriate simulation, with 1,000 repetitions, and produce a null distribution. This distribution represents: Select one: A. Repeated results if the player makes more than 75% of his shots in the long run B. Repeated results if the player makes 80% of his shots in the long run C. Repeated results if the player makes more than 80% of his shots in the long run D. Repeated results if the player makes 75% of his shots in the long run

d

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 standard deviation of your distribution of sample proportions to be approximately which of the following? Select one: A. 0.020 B. 0.400 C. 0.010 D. 0.098

d

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

d

The simulation (flipping coins or using the applet) done to develop the distribution we use to find our p-values assumes which hypothesis is true? Select one: A. Both hypotheses B. Alternative hypothesis C. Neither hypothesis D. Null hypothesis

d

Twenty-nine college students were asked how many states in the U.S. they have been to and the results are shown below. 1, 3, 3, 5, 6, 8, 9, 10, 11, 12, 12, 12, 13, 13, 14, 15, 16, 16, 19, 21, 23, 23, 25, 25, 27, 28, 30, 30, 30 Suppose one of the 30s in the data set was changed to 40. Which of the following statistics would NOT change? Select one: A. The mean, median, and standard deviation would all change B. standard deviation C. mean D. median

d

When using the coin-flipping chance model, the most important reason you repeat a simulation of the study many times is: Select one: A. To see whether the null distribution is centered at 0.50 B. To see whether the null distribution follows a symmetric, bellshaped curve C. To see whether your coin is really fair D. To see how much variability there is in the null distribution

d

When we get a p-value that is very small, we may conclude that: Select one: A. The null hypothesis is plausible. B. The alternative hypothesis has been proven to be false. C. The null hypothesis has been proven to be true. D. There is strong evidence for the alternative hypothesis.

d

Which of the following is NOT true about theory- based confidence intervals for a population proportion? Select one: A. They can be calculated using different confidence levels. B. They should only be used when you have at least 10 successes and 10 failures in your sample data. C. The process used to construct the interval relies on a normal distribution. D. For a given sample proportion, sample size, and confidence level, different intervals can be obtained because of their random nature.

d

A one-sample t-test gives more valid p-values with: Select one: A. Smaller sample sizes and sample distributions that are fairly bell-shaped B. Larger sample sizes and sample distributions that are fairly skewed C. Smaller sample sizes and sample distributions that are fairly skewed D. Any sample size with any shaped sample distributions E. Larger sample sizes and sample distributions that are fairly bell-shaped

e

According to a 2018 report by the U.S. Department of Labor, civilian Americans spend 2.84 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. Suppose that for a random sample of 100 Cal Poly students, the mean and standard deviation of hours per day spent watching TV turns out to be 3.01 and 1.97 hours, respectively. The data were used to find a 95% confidence interval: (2.619, 3.401) hours/day. Which are valid interpretations of the 95% confidence interval? Select one: A. About 95% of all Cal Poly students spend between 2.619 and 3.401 hours/day watching TV. B. There is a 95% chance that, on average, Cal Poly students spend between 2.619 and 3.401 hours/day watching TV. C. We are 95% confident that, on average, these 100 Cal Poly students spend between 2.619 and 3.401 hours/day watching TV. D. In the long run, 95% of the sample means will be between 2.619 and 3.401 hours. E. None of the above.

e

Suppose you are testing the hypotheses H0: π = 0.50 and Ha: π > 0.50 and get a sample proportion of 0.65. From this, you compute a standardized statistic and a p-value. If your sample proportion had been 0.70 then your standardized statistic would (increase/decrease) and your p-value would (increase/decrease)

increase, decrease

Suppose you are testing the hypotheses H0: π = 0.50 versus Ha: π > 0.50. You get a sample proportion of 0.68 and find that your p-value is 0.02. Now suppose you redid your study with each of the following changes, will your new p-value be larger, smaller, or stay the same as the 0.02 you first obtained? Be sure to explain your reasoning. a. Keeping the sample size the same, you take a new sample and find a sample proportion of 0.66. -The new p-value will be (larger/the same/ smaller) because (the sample proportion is closer to the hypothesized long-run proportion value of 0.50/ the center of the null distribution will remain at 0.50/ the sample proportion is farther away from the hypothesized long-run proportion value of 0.50)

larger, the sample proportion is closer to the hypothesized long-run proportion value of 0.50

Suppose you are testing the hypotheses H0: π = 0.50 versus Ha: π > 0.50. You get a sample proportion of 0.68 and find that your p-value is 0.02. Now suppose you redid your study with each of the following changes, will your new p-value be larger, smaller, or stay the same as the 0.02 you first obtained? Be sure to explain your reasoning. You increase the sample size and still find a sample proportion of 0.68. The new p-value will be (larger/the same/smaller) because (it is more likely to get extreme values of the statistic from a larger sample/ it is less likely to get extreme values of the statistic from a larger sample/ increasing the sample size has no effect on the p-value

smaller, it is less likely to get extreme values of the statistic from a larger sample