# Quiz 13: Inference Without Normality

Statistics

Q 1Q 1

Use the following information to answer the question. Suppose the manager of a large furniture store wants to estimate the amount spent by customers during the holiday season. She took a random sample of customers and recorded the amount they spent. A histogram of the data shows that the data is strongly left- skewed. The figures below show the confidence intervals for the mean amount spent using (A)raw (untransformed)data, and (B)log- transformed data, which showed a more normally distributed data set. Use this information to answer the question.
-Calculate the width of both intervals (note that you will need to convert the log- transformed interval back into dollars). Which interval is narrower?
A)Width of interval for untransformed data: 144.2; width of interval for transformed data: 129.8. The width of the interval for the log transformed data is narrower.
B)Width of interval for untransformed data: 72.1; width of interval for transformed data: 273. The width of the interval for the log transformed data is narrower.
C)Width of interval for untransformed data: 144.2; width of interval for transformed data: 152.5. The width of the interval for the untransformed data is narrower.
D)Cannot be determined with the given information

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Multiple Choice

A

Q 2Q 2

Use the following information to answer the question. Math self- efficacy can be defined as one's belief in his or her own ability to perform mathematical tasks. A college math professor wishes to find out if her female students' math self- efficacy matches reality. To do this she gives a math quiz to the female students then asks them to rate their level of confidence in how well they did on the quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume that all conditions for a randomization test have been satisfied.
-Carry out the randomization test. What is the professor's conclusion? Are differences in mean quiz scores due to chance?
A)Fail to reject H0. The professor should conclude that there is no difference in mean quiz scores for those with high confidence and those with low confidence. The student's self- efficacy does not match reality.
B)Reject H0. The professor should conclude that there is no difference in mean quiz scores for those with high confidence and those with low confidence. The student's self- efficacy does not match reality.
C)Fail to reject H0. The professor should conclude that typical quiz scores for those with high confidence is less than that of those with low confidence. The student's self- efficacy matches reality.
D)Reject H0. The professor should conclude that typical quiz scores for those with high confidence is greater than that of those with low confidence. The student's self- efficacy matches reality.

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Multiple Choice

D

Q 3Q 3

Which of the following QQ plots most closely depicts data from a normally distributed population?
A)
B)
C)
D)

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Multiple Choice

D

Q 4Q 4

Use the following information to answer the question. Suppose the manager of a large furniture store wants to estimate the amount spent by customers during the holiday season. She took a random sample of customers and recorded the amount they spent. A histogram of the data shows that the data is strongly left- skewed. The figures below show the confidence intervals for the mean amount spent using (A)raw (untransformed)data, and (B)log- transformed data, which showed a more normally distributed data set. Use this information to answer the question.
-Choose the statement that explains which confidence interval more precisely depicts the data and why.
A)The confidence interval for the untransformed data is more precise because the values are in actual dollars which is more meaningful.
B)The confidence interval for the geometric mean is more precise because the distribution of the log- transformed data is more symmetric.
C)The confidence interval for the untransformed data is more precise because it is strongly left- skewed and the confidence interval gives a wider interval.
D)None of these.

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Multiple Choice

Q 5Q 5

In the context of nonparametric inference, what information can the QQ provide?
A)It is a tool that can help you determine whether a sample is drawn from a normal population.
B)It is a tool that displays quartile locations of data values which can provide information about the sample distribution.
C)It is tool that displays the distribution of transformed data.
D)None of these

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Multiple Choice

Q 6Q 6

Use the following information to answer the question. Math self- efficacy can be defined as one's belief in his or her own ability to perform mathematical tasks. A college math professor wishes to find out if her students' math self- efficacy matches reality. To do this she gives a math quiz then asks her students to rate their level of confidence in how well they did on the quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume that all conditions for a randomization test have been satisfied.
-Use the histogram to roughly estimate the p- value. Choose the answer that most closely approximates the p- value. (Approximations have been made to the nearest hundredth.)
A)p = 0.40
B)p = 0.00
C)p = 0.90
D)None of these

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Multiple Choice

Q 7Q 7

State the null and alternative hypothesis and also the value of the test statistic for the professor's randomization test.
A)H0: The typical quiz score for those with high confidence is the same as that of those with low confidence. H

_{A}: The typical quiz score for those with high confidence is greater than that of those with low confidence. The Test Statistic is 1.2. B)H0: The typical quiz score for those with high confidence is the same as that of those with low confidence. H_{A}: The typical quiz score for those with high confidence is greater than that of those with low confidence. The Test Statistic is 5.4. C)H0: The typical quiz score for those with high confidence is the same as that of those with low confidence. H_{A}: The typical quiz score for those with high confidence is greater than that of those with low confidence. The Test Statistic is - 5.4. D)H0: The typical quiz score for those with high confidence is greater than that of those with low confidence. H_{A}: The typical quiz score for those with high confidence is the same as that of those with low confidence. The Test Statistic is 5.4.Free

Multiple Choice

Q 8Q 8

Find the mean, median, and geometric mean for the following numbers: 10, 300, 1500, and 33,000. Round to the nearest tenth.
A)900.0, 1000.0, 8700.0
B)8700.0, 620.8, 950.0
C)8702.5, 900.0, 620.8
D)8702.5, 900.0, 29.2

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Multiple Choice

Q 9Q 9

Which of the following QQ plots most closely depicts data from a skewed population?
A)
B)
C)
D)

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Multiple Choice

Q 10Q 10

Which of the following statements could be a reason to justify the use of the sign test?
A)The data are matched pairs
B)The sample size is small
C)The distribution of the population is unknown or not Normal
D)All of these

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Multiple Choice

Q 11Q 11

Use the following information to answer the question. Suppose the Nielson Organization conducted a survey to find out how many minutes of televised sporting events people watched in one week. Assume that all conditions for the Mann- Whitney test have been met. Use the following test output to answer the question.
-Using a significance level of 5%, state the correct decision regarding the null hypothesis and the concluding statement.
A)Reject H0. There is evidence to suggest that there is difference in the median amount of televised sporting events that adults in the two age groups watched.
B)Fail to reject H0. There is evidence to suggest that there is a difference in the median amount of televised sporting events that adults in the two age groups watched.
C)Reject H0. There is evidence to suggest that there is no difference in the median amount of televised sporting events that adults in the two age groups watched.
D)Fail to reject H0. There is evidence to suggest that there is no difference in the median amount of televised sporting events that adults in the two age groups watched.

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Multiple Choice

Q 12Q 12

Choose the correct null and alternative hypothesis to test the claim that adults between the ages of 24 and 34 and adults between the ages of 35 and 45 watch different amounts of televised sporting events.
A)H0: The median for adults ages 24 to 34 is equal to the median for adults ages 35 to 45. HA: The median for adults ages 24 to 34 is greater than the median for adults ages 35 to 45.
B)H0: The median for adults ages 24 to 34 is equal to the median for adults ages 35 to 45. HA: The median for the two age groups are not equal.
C)H0: The median for the two age groups are not equal. H

_{A}: The median for adults ages 24 to 34 is equal to the median for adults ages 35- 45. D)H0: The median for adults ages 24 to 34 is equal to the median for adults ages 35 to 45. HA: The median for adults ages 24 to 34 is less than the median for adults ages 35 to 45.Free

Multiple Choice

Q 13Q 13

Which of the following statements is not true about the sign test?
A)The binomial model is used to find an exact p- value.
B)Matched pairs must be independent of other pairs in the sample.
C)The p- value is based on the normal distribution.
D)The sign test relies on the signs (negative or positive)of the measured differences in pairs.

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Multiple Choice

Q 14Q 14

In the context of nonparametric inference, what information can the QQ provide?
A)It is tool that displays the distribution of transformed data.
B)It is a tool that displays quartile locations of data values which can provide information about the sample distribution.
C)It is a tool that can help you determine whether a sample is drawn from a normal population.
D)None of these

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Multiple Choice

Q 15Q 15

Use the following information to answer the question. Suppose the Nielson Organization conducted a survey to find out how many minutes of reality- type television programming people watched in one week. Assume that all conditions for the
Mann- Whitney test have been met. Use the following test output to answer the question.
-Choose the correct null and alternative hypothesis to test the claim that men and women watch different amounts of reality- type programming.
A)H0: The median for men and women are not equal. H

_{A}: The median for men is equal to the median for women. B)H0: The median for men is equal to the median for women. HA: The median for men is less than the median for women. C)H0: The median for men is equal to the median for women. HA: The median for men and women are not equal. D)H0: The median for men is equal to the median for women. HA: The median for men is greater than the median for women.Free

Multiple Choice

Q 16Q 16

A used car lot owner wanted to estimate the amount spent by customers during the summer months. She took a random sample of customers and recorded the amount they spent. A histogram showed the data was right- skewed so she took the log of each value and verified that the distribution of these values was more Normally distributed. What test/method should she use to estimate the mean amount spent during the summer months?
A)Mann- Whitney Test
B)Data transformation
C)Paired t- test
D)Sign Test

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Multiple Choice

Q 17Q 17

Use the following information to answer the question. Can deep- knee bends help you stay alert in class? Forty subjects were measured for alertness at the beginning of class then voluntarily performed fifteen deep- knee bends followed by a forty- five minute lecture. Each subject was then measured for alertness at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met:
-Choose the correct null and alternative hypothesis.
A)H0: The median difference in alertness is 1. HA: The median difference in alertness is not 1.
B)H0: The median difference in alertness is not 0. HA: The median difference in alertness is 0.
C)H0: The median difference in alertness is 0. HA: The median difference in alertness is not 0.
D)None of these.

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Multiple Choice

Q 18Q 18

Use the following information to answer the question. Can stretching help you stay alert in class? Thirty- six subjects were measured for alertness at the beginning of class; the subjects then participated in some light arm and neck stretches followed by a forty- five minute lecture. Each subject was then measured for alertness at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met:
-What is the name and value of the test statistic?
A)Z = 12
B)F = 20
C)S = 20
D)S = 12

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Multiple Choice

Q 19Q 19

Choose the statement that is not true about the Mann- Whitney Test.
A)The Mann- Whitney Test is used to compare the centers of two groups of numerical variables.
B)The Mann- Whitney Test can be used when the Normal condition of the t- test is not met.
C)The Mann- Whitney Test is based on the ranks of the observations, not on their actual values.
D)The Mann- Whitney Test is based on the number of pairs with negative differences.

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Multiple Choice

Q 20Q 20

Which of the following is an indication that nonparametric inference might be necessary?
A)The data is strongly skewed.
B)The sample size is too small to assume the CLT holds.
C)The distribution of the population is not Normal.
D)All of these are indications that nonparametric inference might be necessary.

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Multiple Choice

Q 21Q 21

Use the following information to answer the question. Suppose the manager of a large high- end jewelry store wants to estimate the amount spent by customers during the holiday season. She took a random sample of customers and recorded the amount they spent. A histogram of the data shows that the data is strongly left- skewed. The figures below show the confidence intervals for the mean amount spent using (A)raw (untransformed)data, and (B)log- transformed data, which showed a more normally distributed data set. Use this information to answer the question.
-Choose the statement that explains which confidence interval is likely to be a more precise estimate of amount spent and why.
A)The confidence interval for the geometric mean is more precise because the distribution of the log- transformed data is more symmetric.
B)The confidence interval for the untransformed data is more precise because the values are in actual dollars which is more meaningful.
C)The confidence interval for the untransformed data is more precise because it is strongly left- skewed and the confidence interval gives a wider interval.
D)None of these.

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Multiple Choice

Q 22Q 22

Calculate the width of both intervals (note that you will need to convert the log- transformed interval back into dollars). Which interval is narrower?
A)Width of interval for untransformed data: 55.6; width of interval for transformed data: 111.2. The width of the interval for the log transformed data is narrower.
B)Cannot be determined with the given information
C)Width of interval for untransformed data: 111.2; width of interval for transformed data: 204.6. The width of the interval for the untransformed data is narrower.
D)Width of interval for untransformed data: 111.2; width of interval for transformed data: 92.7. The width of the interval for the log transformed data is narrower.

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Multiple Choice

Q 23Q 23

A new fiber bar is advertised to curb hunger for three hours. A sample of thirty- six hungry subjects were asked to record their level of hunger before eating the fiber bar and again three hours after eating the fiber bar. Which test should be used to test the hypothesis there is no difference in the level of hunger three hours after eating the fiber bar (i.e. the fiber bar curbed hunger for three hours)?
A)Mann- Whitney Test
B)Data transformation
C)Paired t- test
D)Sign Test

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Multiple Choice

Q 24Q 24

Which of the following statements could be a reason to justify the use of the sign test?
A)The data are matched pairs
B)The distribution of the population is unknown or not Normal
C)The sample size is small
D)All of these

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Multiple Choice

Q 25Q 25

Find the mean, median, and geometric mean for the following numbers: 120, 400, 1300, and 22,000. List from smallest to largest and round to the nearest tenth.
A)400.0, 1082.4, 9273.8
B)9273.8, 850.0, 1082.4
C)9300.0, 850.0, 120.0
D)4765.0, 850.0, 1185.5

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Multiple Choice

Q 26Q 26

Use the following information to answer the question. Can stretching help you stay alert in class? Thirty- six subjects were measured for alertness at the beginning of class; the subjects then participated in some light arm and neck stretches followed by a forty- five minute lecture. Each subject was then measured for alertness at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met:
-Choose the correct null and alternative hypothesis.
A)H0: The median difference in alertness is 1. HA: The median difference in alertness is not 1.
B)H0: The median difference in alertness is not 0. HA: The median difference in alertness is 0.
C)H0: The median difference in alertness is 0. HA: The median difference in alertness is not 0.
D)None of these.

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Multiple Choice

Q 27Q 27

Use the following information to answer the question. Can deep- knee bends help you stay alert in class? Forty subjects were measured for alertness at the beginning of class then voluntarily performed fifteen deep- knee bends followed by a forty- five minute lecture. Each subject was then measured for alertness at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met:
-Using a significance level of 5%, state the correct decision regarding the null hypothesis and concluding statement.
A)Reject H0. There is evidence to suggest that there is difference in alertness after deep knee bends before the lecture.
B)Fail to reject H0. There is evidence to suggest that there is a difference in alertness after deep knee bends before the lecture.
C)Fail to reject H0. There is evidence to suggest that there is no difference in alertness after deep knee bends before the lecture.
D)Reject H0. There is evidence to suggest that there is no difference in alertness after deep knee bends before the lecture.

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Multiple Choice

Q 28Q 28

A used car lot owner wanted to estimate the amount spent by customers during the summer months. She took a random sample of customers and recorded the amount they spent. A histogram showed the data was right- skewed so she took the log of each value and verified that the distribution of these values was more Normally distributed. What test/method should she use to estimate the mean amount spent during the summer months?
A)Mann- Whitney Test
B)Paired t- test
C)Sign Test
D)Data transformation and t- interval

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Multiple Choice

Q 29Q 29

Use the following information to answer the question. Can stretching help you stay alert in class? Thirty- six subjects were measured for alertness at the beginning of class; the subjects then participated in some light arm and neck stretches followed by a forty- five minute lecture. Each subject was then measured for alertness at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met:
-Using a significance level of 5%, state the correct decision regarding the null hypothesis and the concluding statement.
A)Reject H0. There is evidence to suggest that there is no difference in alertness after light arm and neck stretches before the lecture.
B)Reject H0. There is evidence to suggest that there is difference in alertness after light arm and neck stretches before the lecture.
C)Fail to reject H0. There is evidence to suggest that there is no difference in alertness after light arm and neck stretches before the lecture.
D)Fail to reject H0. There is evidence to suggest that there is a difference in alertness after light arm and neck stretches before the lecture.

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Multiple Choice

Q 30Q 30

Choose the statement that is not true about the Mann- Whitney Test.
A)The Mann- Whitney Test can be used when the Normal condition of the t- test is not met.
B)The Mann- Whitney Test is based on the ranks of the observations, not on their actual values.
C)The Mann- Whitney Test is based on the number of pairs with positive differences.
D)The Mann- Whitney Test is used to compare the centers of two groups of numerical variables.

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Multiple Choice

Q 31Q 31

Which of the following statements is not true about the sign test?
A)The p- value is based on the normal distribution.
B)Matched pairs must be independent of other pairs in the sample.
C)The binomial model is used to find an exact p- value.
D)The sign test relies on the signs (negative or positive)of the measured differences in pairs.

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Multiple Choice

Q 32Q 32

Use the following information to answer the question. Math self- efficacy can be defined as one's belief in his or her own ability to perform mathematical tasks. A college math professor wishes to find out if her female students' math self- efficacy matches reality. To do this she gives a math quiz to the female students then asks them to rate their level of confidence in how well they did on the quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume that all conditions for a randomization test have been satisfied.
-State the null and alternative hypothesis and also the value of the test statistic for the professor's randomization test.
A)H0: The typical quiz score for those with high confidence is the same as that of those with low confidence. H

_{A}: The typical quiz score for those with high confidence is greater than that of those with low confidence. The Test Statistic is 15. B)H0: The typical quiz score for those with high confidence is the same as that of those with low confidence. H_{A}: The typical quiz score for those with high confidence is greater than that of those with low confidence. The Test Statistic is - 1.2. C)H0: The typical quiz score for those with high confidence is the same as that of those with low confidence. H_{A}: The typical quiz score for those with high confidence is greater than that of those with low confidence. The Test Statistic is - 15. D)H0: The typical quiz score for those with high confidence is greater than that of those with low confidence. H_{A}: The typical quiz score for those with high confidence is the same as that of those with low confidence. The Test Statistic is - 16.3.Free

Multiple Choice

Q 33Q 33

Use the histogram to roughly estimate the p- value. Choose the answer that most closely approximates the p- value. (Approximations have been made to the nearest hundredth.)
A)p = 0.00
B)p = 0.40
C)p = 0.90
D)None of these

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Multiple Choice

Q 34Q 34

Use the following information to answer the question. Math self- efficacy can be defined as one's belief in his or her own ability to perform mathematical tasks. A college math professor wishes to find out if her students' math self- efficacy matches reality. To do this she gives a math quiz then asks her students to rate their level of confidence in how well they did on the quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume that all conditions for a randomization test have been satisfied.
-Carry out the randomization test. What is the professor's conclusion? Are differences in mean quiz scores due to chance?
A)Reject H0. The professor should conclude that typical quiz scores for those with high confidence is greater than that of those with low confidence. The student's self- efficacy matches reality.
B)Fail to reject H0. The professor should conclude that typical quiz scores for those with high confidence is greater than that of those with low confidence. The student's self- efficacy matches reality.
C)Fail to reject H0. The professor should conclude that there is no difference in mean quiz scores for those with high confidence and those with low confidence. The student's self- efficacy does not match reality.
D)Reject H0. The professor should conclude that there is no difference in mean quiz scores for those with high confidence and those with low confidence. The student's self- efficacy does not match reality.

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Multiple Choice

Q 35Q 35

Which of the following is not necessarily an indication that nonparametric inference might be necessary?
A)The distribution of the population is not Normal.
B)The sample size is too small to assume the CLT holds.
C)Variables must be matched pairs.
D)The data is strongly skewed.

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Multiple Choice

Q 36Q 36

Use the following information to answer the question. Can deep- knee bends help you stay alert in class? Forty subjects were measured for alertness at the beginning of class then voluntarily performed fifteen deep- knee bends followed by a forty- five minute lecture. Each subject was then measured for alertness at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met:
-What is the name and value of the test statistic?
A)S = 21
B)F = 21
C)S = 14
D)Z = 5

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Multiple Choice

Q 37Q 37

Use the following information to answer the question. Suppose the Nielson Organization conducted a survey to find out how many minutes of reality- type television programming people watched in one week. Assume that all conditions for the
Mann- Whitney test have been met. Use the following test output to answer the question.
-Using a significance level of 5%, state the correct decision regarding the null hypothesis and the concluding statement.
A)Fail to reject H0. There is evidence to suggest that there is a difference in the median amount of reality- type television that men and women watch.
B)Fail to reject H0. There is evidence to suggest that there is no difference in the median amount of reality- type television that men and women watch.
C)Reject H0. There is evidence to suggest that there is a difference in the median amount of reality- type television that men and women watch.
D)Reject H0. There is evidence to suggest that there is no difference in the median amount of reality- type television that men and women watch.

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Multiple Choice

Q 38Q 38

A new fiber bar is advertised to curb hunger for three hours. A sample of thirty- six hungry subjects were asked to record their level of hunger before eating the fiber bar and again three hours after eating the fiber bar. Which test should be used to test the hypothesis there is no difference in the level of hunger three hours after eating the fiber bar (i.e. the fiber bar curbed hunger for three hours)?
A)Paired t- test
B)Sign Test
C)Data transformation
D)Mann- Whitney Test

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Multiple Choice

Q 39Q 39

You are presented with data from two independent samples. The variable being measured is continuous. The distribution of the population of each sample is right skewed. You wish to test the hypothesis that there is a difference in the median value of the variable for the samples. What type test/method should you use?
A)Mann- Whitney Test
B)Data transformation
C)Paired t- test
D)Sign Test

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Multiple Choice

Q 40Q 40

You are presented with data from two independent samples. The variable being measured is continuous. The distribution of the population of each sample is right skewed. You wish to test the hypothesis that there is a difference in the median value of the variable for the samples. What type test/method should you use?
A)Mann- Whitney Test
B)Sign Test
C)Paired t- test
D)Data transformation and t- interval

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Multiple Choice

Q 41Q 41

Use the following information to answer the question. Can dogs lower anxiety in math class? Fifty subjects who reported anxiety about attending math class were measured for stress at the beginning of a math class then spent 15 minutes interacting with a dog followed by a forty- five minute math lecture. Each subject was then measured for stress at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met:
-Explain how the binomial model is used to calculate the p- value.

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Essay

Q 42Q 42

State the null and alternative hypothesis to test the claim that dogs can affect anxiety levels.

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Essay

Q 43Q 43

Suppose data was collected from ten women and twelve men about the length in minutes of their commute to work. The histogram for men was roughly normal, but the histogram for women was strongly skewed to the right. Explain why the t- test is not appropriate to test whether men and women have different commute times.

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Essay

Q 44Q 44

Use the following information to answer the question. Math self- efficacy can be defined as one's belief in his or her own ability to perform mathematical tasks. A college math professor wishes to find out if her male students' math self- efficacy matches reality. To do this she gives a math quiz to the male students then asks them to rate their level of confidence in how well they did on the quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume that all conditions for a randomization test have been satisfied.
-State the null and alternative hypothesis and also the value of the test statistic for the professor's randomization test.

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Essay

Q 45Q 45

Use the following information to answer the question. Suppose the Nielson Organization conducted a survey to find out how many minutes of crime dramas that people watched in one week. Assume that all conditions for the Mann- Whitney test have been met. Use the following test output to answer the question.
-Using a significance level of 5%, state the correct decision regarding the null hypothesis and write a sentence which summarizes the conclusion and addresses the claim.

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Essay

Q 46Q 46

Use the following information to answer the question. Suppose the manager of a large appliance and electronics store wants to estimate the amount spent by customers during the holiday season. He took a random sample of customers and recorded the amount they spent. A histogram of the data shows that the data is strongly left- skewed. The figures below show the confidence intervals for the mean amount spent using (A)raw (untransformed)data, and (B)log- transformed data, which showed a more normally distributed data set.
-Calculate the width of both intervals (note that you will need to convert the
log- transformed interval back into dollars)and state which interval is narrower?

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Essay

Q 47Q 47

Use the following information to answer the question. Math self- efficacy can be defined as one's belief in his or her own ability to perform mathematical tasks. A college math professor wishes to find out if her male students' math self- efficacy matches reality. To do this she gives a math quiz to the male students then asks them to rate their level of confidence in how well they did on the quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume that all conditions for a randomization test have been satisfied.
-Explain how you would use the histogram to get an approximate p- value and state your p- value estimation.

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Essay

Q 48Q 48

Use the following information to answer the question. Math self- efficacy can be defined as one's belief in his or her own ability to perform mathematical tasks. A college math professor wishes to find out if her male students' math self- efficacy matches reality. To do this she gives a math quiz to the male students then asks them to rate their level of confidence in how well they did on the quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume that all conditions for a randomization test have been satisfied.
-Explain some factors that might indicate that nonparametric inference might be necessary.

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Essay

Q 49Q 49

Use the following information to answer the question. Can dogs lower anxiety in math class? Fifty subjects who reported anxiety about attending math class were measured for stress at the beginning of a math class then spent 15 minutes interacting with a dog followed by a forty- five minute math lecture. Each subject was then measured for stress at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met:
-Using a significance level of 5%, state the correct decision regarding the null hypothesis and write a sentence which summarizes the conclusion and addresses the claim.

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Essay

Q 50Q 50

For which sample might a log transform be useful? Explain. (There are no zeros or negative values in either data set.)

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Essay

Q 51Q 51

List three of the five conditions, pertaining to the sample, which must be met in order to use the Mann- Whitney test.

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Q 52Q 52

Calculate the mean, median, and geometric mean for the following numbers: 110, 500, 1700, and 31,000. List from smallest to largest and round to the nearest tenth.

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Q 53Q 53

Suppose you are asked to analyze sample data but you do not know the distribution of the population it came from. Explain how a QQ plot can be used to give you information about the population from which the samples was drawn.

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Q 54Q 54

Match the histogram with the corresponding QQ plot.
Histogram (a)goes with QQ plot .
Histogram (b)goes with QQ plot .

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Q 56Q 56

Use the following information to answer the question. Can dogs lower anxiety in math class? Fifty subjects who reported anxiety about attending math class were measured for stress at the beginning of a math class then spent 15 minutes interacting with a dog followed by a forty- five minute math lecture. Each subject was then measured for stress at the end of the lecture. The hypothesis test results for the sign test are summarized below. Assume that all conditions for testing have been met:
-Calculate the value of the test statistic and state the value of the p- value.

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Q 57Q 57

Use the following information to answer the question. Suppose the Nielson Organization conducted a survey to find out how many minutes of crime dramas that people watched in one week. Assume that all conditions for the Mann- Whitney test have been met. Use the following test output to answer the question.
-State the null and alternative hypothesis to test the claim that adults between the ages of 24 and 39 and adults between the ages of 40 and 55 watch different amounts of crime dramas on television.

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Q 58Q 58

Use the following information to answer the question. Suppose the manager of a large appliance and electronics store wants to estimate the amount spent by customers during the holiday season. He took a random sample of customers and recorded the amount they spent. A histogram of the data shows that the data is strongly left- skewed. The figures below show the confidence intervals for the mean amount spent using (A)raw (untransformed)data, and (B)log- transformed data, which showed a more normally distributed data set.
-Which interval should the manager report to the store owner about the typical amount of money spent during the holiday season? Explain.

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Q 59Q 59

Use the following information to answer the question. Math self- efficacy can be defined as one's belief in his or her own ability to perform mathematical tasks. A college math professor wishes to find out if her male students' math self- efficacy matches reality. To do this she gives a math quiz to the male students then asks them to rate their level of confidence in how well they did on the quiz. She plans to test whether those who had little confidence that they did well on the quiz actually performed worse than those who had a high level of confidence that they did well on the quiz. Shown below is the approximate sampling distribution of the difference in mean quiz scores. The table below shows the summary statistics for the two groups. Assume that all conditions for a randomization test have been satisfied.
-Complete the randomization test by stating the proper decision regarding the null hypothesis and the professor's conclusion. Are differences in mean quiz scores due to chance?

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