Deck 13: Inference Without Normality

Question 1

Which of the following QQ plots most closely depicts data from a normally distributed population?

Answer 1

D

Question 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 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. $\begin{array}{l}\begin{array} { | l | c | c | c | c | c | } \hline { \text { Group } } & \mathrm { n } & \text { Mean } & \text { Median } & \begin{array} { c } \text { Standard } \\\text { Deviation }\end{array} & \text { IQR } \\\hline \text { High Conf. } & 106 & 78.6 & 77.5 & 5.5 & 9.5 \\\hline \text { Low Conf. } & 211 & 73.2 & 72.5 & 4.2 & 8.3 \\\hline\end{array}\\\hline \text { Test Stat: Mean High Conf. - Mean Low Conf. } \\\hline \text { Number of simulations: } 350 \\\end{array}$


-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

Answer 2

$p=0.40$

Question 3

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: Hypothesis test results:
Parameter: Median of variable
$\begin{array}{l}H_{0}: \text { median }=0 \\H_{A}: \text { median } \neq 0\end{array}$
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \text { Variable } & \mathrm{n} & \mathrm{n} \text { for tests } & \text { Sample Median } & \text { Below } & \text { Equal } & \text { Above } & \text { P-value } \\\hline \text { Difference } & 36 & 32 & 1 & 12 & 4 & 20 & 0.2153 \\\hline\end{array}$

-What is the name and value of the test statistic?

A) $Z=12$
B) $\mathrm{F}=20$
C) $S=20$
D) $S=12$

Answer 3

$S=20$

Question 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. $$\begin{array}{l}\begin{array} { | l l l l l c | } \hline { \text { (A) One-Sample T: Purch } } \\\hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } \\\hline \text { Purch } & 17 & 544.5 & 140.2 & 26.0 & ( 472.4,616.6 ) \\\hline\end{array}\\\\\begin{array} { | l c c c c c | } \hline { \text { B) One-Sample T: LogPurch } } \\\hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } \\\hline \text { LogPurch } & 17 & 2.73 & 0.121 & 0.101 & ( 2.7,2.8 ) \\\hline\end{array}\end{array}$$

-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

Question 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

Question 6

State the null and alternative hypothesis and also the value of the test statistic for the professor's randomization test.

Question 7

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. $$\begin{array}{l}\begin{array} { | l l l l l c | } \hline { \text { (A) One-Sample T: Purch } } \\\hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } \\\hline \text { Purch } & 17 & 544.5 & 140.2 & 26.0 & ( 472.4,616.6 ) \\\hline\end{array}\\\\\begin{array} { | l c c c c c | } \hline { \text { B) One-Sample T: LogPurch } } \\\hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } \\\hline \text { LogPurch } & 17 & 2.73 & 0.121 & 0.101 & ( 2.7,2.8 ) \\\hline\end{array}\end{array}$$

-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.

Question 8

Which of the following QQ plots most closely depicts data from a skewed population?

Question 9

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

Question 10

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: Hypothesis test results:
Parameter: Median of variable
$\begin{array}{l}H_{0}: \text { median }=0 \\H_{A}: \text { median } \neq 0\end{array}$
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \text { Variable } & \mathrm{n} & \mathrm{n} \text { for tests } & \text { Sample Median } & \text { Below } & \text { Equal } & \text { Above } & \text { P-value } \\\hline \text { Difference } & 40 & 35 & 1 & 14 & 5 & 21 & 0.4777 \\\hline\end{array}$

-Choose the correct null and alternative hypothesis.

A) $\mathrm{H}_{0}$ : The median difference in alertness is 1 . $\mathrm{H}_{\mathrm{A}}$ : The median difference in alertness is not 1 .
B) $\mathrm{H}_{0}$ : The median difference in alertness is not 0 . $\mathrm{H}_{\mathrm{A}}$ : The median difference in alertness is 0 .
C) $\mathrm{H}_{0}$ : The median difference in alertness is 0 . $\mathrm{H}_{\mathrm{A}}$ : The median difference in alertness is not 0 .
D) None of these.

Question 11

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.

Question 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.

Question 13

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

Question 14

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.

Question 15

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

Question 16

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. $\begin{array}{l}\begin{array} { | l | c | c | c | c | c | } \hline { \text { Group } } & \mathrm { n } & \text { Mean } & \text { Median } & \begin{array} { c } \text { Standard } \\\text { Deviation }\end{array} & \text { IQR } \\\hline \text { High Conf. } & 106 & 77.2 & 75.5 & 6.5 & 10.5 \\\hline \text { Low Conf. } & 211 & 62.2 & 59.2 & 5.9 & 9.3 \\\hline\end{array}\\\hline \text { Test Stat: Mean High Conf. } - \text { Mean Low Conf. } \\\hline \text { Number of simulations: } 350 \\\end{array}$


-Carry out the randomization test. What is the professor's conclusion? Are differences in mean quiz scores due to chance?

A) Fail to reject $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . 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.

Question 17

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 test have been met. Use the following test output to answer the question. Hypothesis test results:
$\mathrm{ml}=$ median for adults ages $24-34$
$\mathrm{m} 2=$ median for adults ages $35-45$
Parameter: $\mathrm{m} 1-\mathrm{m} 2$
$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Difference } & \mathrm{n} 1 & \mathrm{n} 2 & \text { Diff.Est } & \text { Test Stat } & \text { P-value } & \text { Method } \\\hline \mathrm{m} 1-\mathrm{m} 2 & 12 & 12 & 65 & 45.7 & 0.120 & \text { Norm. Approx. } \\\hline\end{array}$

-Using a significance level of 5%, state the correct decision regarding the null hypothesis and the concluding statement.

A) Reject $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . 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.

Question 18

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. Hypothesis test results:
$\mathrm{ml}=$ median for women
$\mathrm{m} 2=$ median for men
Parameter: m1-m2
$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Difference } & \mathrm{n} 1 & \mathrm{n} 2 & \text { Diff.Est } & \text { Test Stat } & \text { P-value } & \text { Method } \\\hline \mathrm{m} 1-\mathrm{m} 2 & 10 & 10 & 50 & 38.2 & 0.022 & \text { Norm. Approx. } \\\hline\end{array}$

-Choose the correct null and alternative hypothesis to test the claim that men and women watch different amounts of reality-type programming.

A) $\mathrm{H}_{0}$ : The median for men and women are not equal.
$\mathrm{H}_{\mathrm{A}}$ : The median for men is equal to the median for women.
B) $\mathrm{H}_{0}$ : The median for men is equal to the median for women.
$\mathrm{H}_{\mathrm{A}}$ : The median for men is less than the median for women.
C) $\mathrm{H}_{0}$ : The median for men is equal to the median for women.
$\mathrm{H}_{\mathrm{A}}$ : The median for men and women are not equal.
D) $\mathrm{H}_{0}$ : The median for men is equal to the median for women.
$\mathrm{H}_{\mathrm{A}}$ : The median for men is greater than the median for women.

Question 19

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

Question 20

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.

Question 21

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

Question 22

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: Hypothesis test results:
Parameter: Median of variable
$\begin{array}{l}H_{0}: \text { median }=0 \\H_{A}: \text { median } \neq 0\end{array}$
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \text { Variable } & \mathrm{n} & \mathrm{n} \text { for tests } & \text { Sample Median } & \text { Below } & \text { Equal } & \text { Above } & \text { P-value } \\\hline \text { Difference } & 40 & 35 & 1 & 14 & 5 & 21 & 0.4777 \\\hline\end{array}$

-Using a significance level of 5%, state the correct decision regarding the null hypothesis and concluding statement.

A) Reject $\mathrm{H}_{0}$ . There is evidence to suggest that there is difference in alertness after deep knee bends before the lecture.

B) Fail to reject $\mathrm{H}_{0}$ . There is evidence to suggest that there is a difference in alertness after deep knee bends before the lecture.
C) Fail to reject $\mathrm{H}_{0}$ . There is evidence to suggest that there is no difference in alertness after deep knee bends before the lecture.

D) Reject $\mathrm{H}_{0}$ . There is evidence to suggest that there is no difference in alertness after deep knee bends before the lecture.

Question 23

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. Hypothesis test results:
$\mathrm{ml}=$ median for women
$\mathrm{m} 2=$ median for men
Parameter: m1-m2
$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Difference } & \mathrm{n} 1 & \mathrm{n} 2 & \text { Diff.Est } & \text { Test Stat } & \text { P-value } & \text { Method } \\\hline \mathrm{m} 1-\mathrm{m} 2 & 10 & 10 & 50 & 38.2 & 0.022 & \text { Norm. Approx. } \\\hline\end{array}$

-Using a significance level of 5%, state the correct decision regarding the null hypothesis and the concluding statement.

A) Fail to reject $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . There is evidence to suggest that there is no difference in the median amount of reality-type television that men and women watch.

Question 24

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

Question 25

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.

Question 26

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.

Question 27

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

Question 28

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: Hypothesis test results:
Parameter: Median of variable
$\begin{array}{l}H_{0}: \text { median }=0 \\H_{A}: \text { median } \neq 0\end{array}$
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \text { Variable } & \mathrm{n} & \mathrm{n} \text { for tests } & \text { Sample Median } & \text { Below } & \text { Equal } & \text { Above } & \text { P-value } \\\hline \text { Difference } & 36 & 32 & 1 & 12 & 4 & 20 & 0.2153 \\\hline\end{array}$

-Using a significance level of 5%, state the correct decision regarding the null hypothesis and the concluding statement.

A) Reject $\mathrm{H}_{0}$ . There is evidence to suggest that there is no difference in alertness after light arm and neck stretches before the lecture.

B) Reject $\mathrm{H}_{0}$ . There is evidence to suggest that there is difference in alertness after light arm and neck stretches before the lecture.

C) Fail to reject $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . There is evidence to suggest that there is a difference in alertness after light arm and neck stretches before the lecture.

Question 29

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. $$\begin{array}{l}\begin{array} { | l | c | c | c | c | c | } \hline { \text { Group } } & \mathrm { n } & \text { Mean } & \text { Median } & \begin{array} { c } \text { Standard } \\\text { Deviation }\end{array} & \text { IQR } \\\hline \text { High Conf. } & 106 & 77.2 & 75.5 & 6.5 & 10.5 \\\hline \text { Low Conf. } & 211 & 62.2 & 59.2 & 5.9 & 9.3 \\\hline\end{array}\\\hline \text { Test Stat: Mean High Conf. - Mean Low Conf. } \\\hline \text { Number of simulations: } 350 \\\end{array}$$


-State the null and alternative hypothesis and also the value of the test statistic for the professor's randomization test.

A) $\mathrm{H}_{0}$ : The typical quiz score for those with high confidence is the same as that of those with low confidence.
$\mathrm{H}_{\mathrm{A}}$ : The typical quiz score for those with high confidence is greater than that of those with low confidence.
The Test Statistic is $15 .$
B) $\mathrm{H}_{0}$ : The typical quiz score for those with high confidence is the same as that of those with low confidence.
$\mathrm{H}_{\mathrm{A}}$ : 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) $\mathrm{H}_{0}$ : The typical quiz score for those with high confidence is the same as that of those with low confidence.
$\mathrm{H}_{\mathrm{A}}$ : The typical quiz score for those with high confidence is greater than that of those with low confidence.
The Test Statistic is $-15$ .
D) $\mathrm{H}_{0}$ : The typical quiz score for those with high confidence is greater than that of those with low confidence.
$\mathrm{H}_{\mathrm{A}}$ : The typical quiz score for those with high confidence is the same as that of those with low confidence.
The Test Statistic is $-16.3$ .

Question 30

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: Hypothesis test results:
Parameter: Median of variable
$\begin{array}{l}H_{0}: \text { median }=0 \\H_{A}: \text { median } \neq 0\end{array}$
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \text { Variable } & \mathrm{n} & \mathrm{n} \text { for tests } & \text { Sample Median } & \text { Below } & \text { Equal } & \text { Above } & \text { P-value } \\\hline \text { Difference } & 36 & 32 &1& 12 & 4 & 20 & 0.2153 \\\hline\end{array}$

-Choose the correct null and alternative hypothesis.

A) $\mathrm{H}_{0}$ : The median difference in alertness is 1 . $\mathrm{H}_{\mathrm{A}}$ : The median difference in alertness is not 1 .
B) $\mathrm{H}_{0}$ : The median difference in alertness is not 0 . $\mathrm{H}_{\mathrm{A}}$ : The median difference in alertness is 0 .
C) $\mathrm{H}_{0}$ : The median difference in alertness is 0 . $\mathrm{H}_{\mathrm{A}}$ : The median difference in alertness is not 0 .
D) None of these.

Question 31

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. $$\begin{array}{l}\begin{array} { | l c c c c c | } \hline { \text { (A) One-Sample T: Purch } } \\\hline \text { Variable } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } \\\hline \text { Purch } & 15 & 223.5 & 100.4 & 26.0 & ( 167.9,279.1 ) \\\hline\end{array}\\\\\begin{array} { | l c c c c c | } \hline { \text { (B) One-Sample T: LogPurch } } \\\hline \text { Variable } & \text { N } & \text { Mean } & \text { StDev } & \text { SE Mean } & 95 \% \text { CI } \\\hline \text { LogPurch } & 15 & 2.311 & 0.236 & 0.101 & ( 2.2,2.4 ) \\\hline\end{array}\end{array}$$

-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.

Question 32

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.

Question 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.)

Question 34

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

Question 35

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

Question 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
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: Hypothesis test results:
Parameter: Median of variable
$\begin{array}{l}H_{0}: \text { median }=0 \\H_{A}: \text { median } \neq 0\end{array}$
$\begin{array}{|l|l|l|l|l|l|l|l|}\hline \text { Variable } & \mathrm{n} & \mathrm{n} \text { for tests } & \text { Sample Median } & \text { Below } & \text { Equal } & \text { Above } & \text { P-value } \\\hline \text { Difference } & 40 & 35 & 1 & 14 & 5 & 21 & 0.4777 \\\hline\end{array}$

-What is the name and value of the test statistic?

A) $S=21$
B) $F=21$
C) $S=14$
D) $Z=5$

Question 37

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. $$\begin{array}{l}\begin{array} { | l | c | c | c | c | c | } \hline { \text { Group } } & \mathrm { n } & \text { Mean } & \text { Median } & \begin{array} { c } \text { Standard } \\\text { Deviation }\end{array} & \text { IQR } \\\hline \text { High Conf. } & 106 & 78.6 & 77.5 & 5.5 & 9.5 \\\hline \text { Low Conf. } & 211 & 73.2 & 72.5 & 4.2 & 8.3 \\\hline\end{array}\\\hline \text { Test Stat: Mean High Conf. } - \text { Mean Low Conf. } \\\hline \text { Number of simulations: } 350 \\\end{array}$$


-Carry out the randomization test. What is the professor's conclusion? Are differences in mean quiz scores due to chance?

A) Reject $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . 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 $\mathrm{H}_{0}$ . 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.

Question 38

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.

Question 39

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

Question 40

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

Question 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:


-Calculate the value of the test statistic and state the value of the p-value.

Question 42

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.

Question 43

Describe some conditions that might indicate that sign test should be used for inference.

Question 44

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.

Question 45

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.

Question 46

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.

Question 47

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.

Question 48

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

Question 49

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

Question 50

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?

Question 51

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.

Question 52

Explain some factors that might indicate that nonparametric inference might be necessary.

Question 53

Refer to the following two histograms and QQ plots of the same data to answer the question.

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

Question 54

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?

Question 55

Refer to the following two histograms and QQ plots of the same data to answer the question.

-Match the histogram with the corresponding QQ plot.

Question 56

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 of test/method should you use?
Explain why the t-test is not appropriate in this situation.

Question 57

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.

Question 58

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.

Question 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.

-Explain how you would use the histogram to get an approximate p-value and state your p-value estimation.

Question 60

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 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.