Question 1

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. $$\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. } & 105 & 82.5 & 84.0 & 7.1 & 12.5 \
\hline \text { Low Conf. } & 201 & 72.1 & 69.9 & 6.2 & 10.4 \

\hline
\end{array}\
\hline \text { Test Stat: Mean High Conf. - Mean Low Conf. } \
\hline \text { Number of simulations: } 350 \
\end{array}$$

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

Accepted Answer

To approximate the p-value using the histogram draw a vertical line at about 14.1 then approximate the proportion of observations to the right of the vertical line. From the histogram it appears that there are no observations to the right of 14.1 so the p-value is approximately zero.

Question 2

Which of the following statements is not true about the sign test?

Accepted Answer

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. A

Question 3

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.)

Accepted Answer

A)    p=0.40 p=0.40 p=0.40 
B)    p=0.00 p=0.00 p=0.00 
C)    p=0.90 p=0.90 p=0.90 
D)   None of these  A

Question 4

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?

Accepted Answer

A)   Mann-Whitney Test
B)   Paired t-test
C)   Sign Test
D)   Data transformation and t-interval

Question 5

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?

Accepted Answer

A)   Reject  H0 \mathrm{H}_{0} 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 \mathrm{H}_{0} 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 \mathrm{H}_{0} 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 \mathrm{H}_{0} 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.

Question 6

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.

Accepted Answer

The answer of Suppose you are asked to analyze sample...

Question 7

Which of the following statements is not true about the sign test?

Accepted Answer

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 8

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

Accepted Answer

The answer of State the null and alternative hypothesis to...

Question 9

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.)

Accepted Answer

A)    p=0.00 p=0.00 p=0.00 
B)    p=0.40 p=0.40 p=0.40 
C)    p=0.90 p=0.90 p=0.90 
D)   None of these

Question 10

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.

Accepted Answer

A)    H0 \mathrm{H}_{0} H0​  : The median for men and women are not equal. HA \mathrm{H}_{\mathrm{A}} HA​  : The median for men is equal to the median for women.
B)    H0 \mathrm{H}_{0} H0​  : The median for men is equal to the median for women. HA \mathrm{H}_{\mathrm{A}} HA​  : The median for men is less than the median for women.
C)    H0 \mathrm{H}_{0} H0​  : The median for men is equal to the median for women. HA \mathrm{H}_{\mathrm{A}} HA​  : The median for men and women are not equal.
D)    H0 \mathrm{H}_{0} H0​  : The median for men is equal to the median for women. HA \mathrm{H}_{\mathrm{A}} HA​  : The median for men is greater than the median for women.

Question 11

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

Accepted Answer

The answer of Describe some conditions that might indicate that...

Question 12

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.

Accepted Answer

The answer of Suppose data was collected from ten women...

Question 13

Choose the statement that is not true about the Mann-Whitney Test.

Accepted Answer

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 14

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:
 Hypothesis test results:
Parameter: Median of variable
$
\begin{array}{l}
H_{0}: \text { median }=0 \
H_{A}: \text { median } \neq 0
\end{array}
$
$\begin{array}{|l|l|l|l|l|l|l|l|}
\hline \text { Variable } & \mathrm{n} & \mathrm{n} \text { for tests } & \text { Sample Median } & \text { Below } & \text { Equal } & \text { Above } & \text { P-value } \
\hline \text { Difference } & 50 & 46 & 1 & 18 & 4 & 28 & 0.1839 \
\hline
\end{array}$
-Explain how the binomial model is used to calculate the p-value.

Accepted Answer

The answer of Use the following information to answer the...

Question 15

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.

Accepted Answer

A)    H0 \mathrm{H}_{0} H0​  : The median difference in alertness is 1 .  HA \mathrm{H}_{\mathrm{A}} HA​  : The median difference in alertness is not 1 .
B)    H0 \mathrm{H}_{0} H0​  : The median difference in alertness is not 0 .  HA \mathrm{H}_{\mathrm{A}} HA​  : The median difference in alertness is 0 .
C)    H0 \mathrm{H}_{0} H0​  : The median difference in alertness is 0 .  HA \mathrm{H}_{\mathrm{A}} HA​  : The median difference in alertness is not 0 .
D)   None of these.

Question 16

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

Accepted Answer

The answer of List three of the five conditions, pertaining...

Question 17

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)?

Accepted Answer

A)   Mann-Whitney Test
B)   Data transformation
C)   Paired t-test
D)   Sign Test

Question 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: 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.

Accepted Answer

A)   Reject  H0 \mathrm{H}_{0} 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 \mathrm{H}_{0} 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 \mathrm{H}_{0} 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 \mathrm{H}_{0} H0​ . There is evidence to suggest that there is a difference in alertness after light arm and neck stretches before the lecture.

Question 19

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

Accepted Answer

A)   
B)  
C)  
D)

Question 20

Which of the following statements could be a reason to justify the use of the sign test?

Accepted Answer

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

Exam 13: Inference Without Normality

Which of the following statements is not true about the sign test?

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.

Which of the following statements is not true about the sign test?

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

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.)

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

Choose the statement that is not true about the Mann-Whitney Test.

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

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

Which of the following statements could be a reason to justify the use of the sign test?