Question 1

A statistician performs a Mann-Whitney test to compare the means of two populations using independent simple random samples. Suppose that the sum of the ranks for sample 1 is much larger than the sum of the ranks for sample 2 . Explain in your own words what this suggests about the relationship between $\mu _ { 1 }$ and $\mu _ { 2 }$.

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Question 2

Independent simple random samples of sizes 120 and 150 are taken from two populations with the intent of performing a hypothesis test to compare the means. Prior data analyses have indicated that the two population standard deviations are equal; however, the variable under consideration is not normally distributed on either population. Is it reasonable to use the pooled t-test in this situation? Explain your answer.

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Question 3

A researcher wants to compare the mean systolic blood pressures for adults ages 20-29 and adults ages 30-39. Identify the variable under consideration and the two populations. Suppose the researcher wants to perform a hypothesis test to decide whether the mean systolic blood pressure for adults aged 20-29 is lower than the mean systolic blood pressure for adults aged 30-39. State the null and alternative hypotheses for the hypothesis test.

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The answer of A researcher wants to compare the mean...

Question 4

Preliminary data analyses indicates that use of a paired t-test is reasonable. Perform the hypothesis test by using eitherthe critical-value approach or the P-value approach as indicated. Assume that the null hypothesis is  $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-Five students took a math test before and after tutoring. Their scores were as follows. $$\begin{array} { c | r r r r r }  \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \ \hline \text { Before } & 71 & 78 & 73 & 72 & 75 \ \hline \text { After } & 75 & 87 & 71 & 75 & 87 \end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the mean score before tutoring differs from the mean score after tutoring? Use the P-value approach.

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The answer of Preliminary data analyses indicates that use of...

Question 5

Suppose that you want to perform a hypothesis test based on independent simple random samples to compare the means of two populations. Assume that the variable under consideration is uniformly distributed on both of the populations and that the two population standard deviations are equal. Both sample sizes are small. Identify the procedures that could be used to carry out the hypothesis test, that is, the procedures whose assumptions are satisfied. If more than one procedure could be used, which one would be the best? Explain your answer.

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Question 6

Suppose that you want to perform a hypothesis test to compare the means of two populations using paired samples. How would you decide between the paired t-test and the paired Wilcoxon signed-rank test?

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The answer of Suppose that you want to perform a...

Question 7

Preliminary data analyses indicate that you can reasonably use nonpooled t-procedures on the given data. Apply anonpooled t-test to perform the required hypothesis test, using either the critical-value approach or the P-value approachas indicated.
-A researcher was interested in comparing the GPAs of students at two different colleges. Independent random samples of 8 students from college A and 13 students from college B yielded the following GPAs: $$\begin{array} { c | c c } 
\text { College A } &  { \text { College B } } \
\hline 3.7 & 3.8 & 2.8 \
3.2 & 3.2 & 4.0 \
3.0 & 3.0 & 3.6 \
2.5 & 3.9 & 2.6 \
2.7 & 3.8 & 4.0 \
3.6 & 2.5 & 3.6 \
2.8 & 3.9 & \
3.4 & &
\end{array}$$ At the 10% significance level, do the data provide sufficient evidence to conclude that the mean GPA of students at college A differs from the mean GPA of students at college B? Use the P-value approach.  $\text { (Note: } \left. \bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , \mathrm {~s} _ { 1 } = 0.4357 , \mathrm {~s} _ { 2 } = 0.5485 . \right)$

Accepted Answer

The answer of Preliminary data analyses indicate that you can...

Question 8

Suppose that you want to perform a hypothesis test to compare the means of two populations using independent simple random samples. The two distributions of the variable under consideration have the same shape. How would you decide between the pooled t-test and the Mann-Whitney test?

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The answer of Suppose that you want to perform a...

Question 9

Suppose that you want to perform a hypothesis test to compare the means of two populations using a paired sample. Preliminary data analyses of the sample of paired differences suggest that the distribution of the paired-difference variable is skewed to the right . The sample of 20 paired differences contains an outlier. If it is not legitimate to remove the outlier, is it reasonable to use a paired t-test? Is it reasonable to use a paired Wilcoxon signed-rank test? Explain your thinking

Accepted Answer

The answer of Suppose that you want to perform a...

Question 10

Preliminary data analyses indicate that you can reasonably use nonpooled t-procedures on the given data. Apply anonpooled t-test to perform the required hypothesis test, using either the critical-value approach or the P-value approachas indicated.
-A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples of 16 people ages 30-40 who do not exercise regularly and 12 people ages 30-40 who exercise regularly were selected, and the resting pulse rate (in beats per minute)of each person was measured. The summary statistics are as follows.  $\begin{array} { r | r }  \text { Do Not Exercise } & \text { Do Exercise } \ \hline \overline { \mathrm { x } } _ { 1 } = 73.5 & \overline { \mathrm { x } } _ { 2 } = 68.5 \ \mathrm {~s} _ { 1 } = 10.9 & \mathrm {~s} _ { 2 } = 8.2 \ \mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 12 \end{array}$ 
 At the 2.5% significance level, do the data provide sufficient evidence to conclude that the mean resting pulse rate of people who do not exercise regularly is greater than the mean resting pulse rate of people who exercise regularly? Use the critical-value approach.

Accepted Answer

The answer of Preliminary data analyses indicate that you can...

Question 11

Preliminary data analyses indicate that you can reasonably consider the assumptions for using pooled t-proceduressatisfied. Perform the required hypothesis test by using either the critical-value approach or the P-value approach asindicated.
-A researcher was interested in comparing the GPAs of students at two different colleges. Independent simple random samples of 8 students from college A and 13 students from college B yielded the following GPAs. $$\begin{array} { r | r }  \text { College A } & \text { College B } \ \hline 3.7 & 3.82 .8 \ 3.2 & 3.24 .0 \ 3.0 & 3.03 .6 \ 2.5 & 3.92 .6 \ 2.7 & 3.84 .0 \ 3.6 & 2.53 .6 \ 2.8 & 3.9 \ 3.4 & \end{array}$$ At the 10% significance level, do the data provide sufficient evidence to conclude that the mean GPA of students at college A differs from the mean GPA of students at college B? Use the critical-value approach.  $\left( \text { Note: } \bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , s _ { 1 } = 0.4357 , s _ { 2 } = 0.5485 . \right)$

Accepted Answer

The answer of Preliminary data analyses indicate that you can...

Question 12

Provide an appropriate response.
-Suppose a researcher wants to perform a hypothesis test to decide whether the mean systolic blood pressure for adults aged 20-29 is lower than the mean systolic blood pressure for adults aged 30-39. State the null and alternative hypotheses for the hypothesis test. Discuss the basic strategy for performing this hypothesis test, based on independent samples.

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The answer of Provide an appropriate response.
-Suppose a researcher wants...

Question 13

The pooled t-test requires the assumption that the two population standard deviations be equal. What methods are available for checking this assumption? Which of these methods is not recommended and why is it not recommended?

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The answer of The pooled t-test requires the assumption that...

Question 14

Preliminary data analyses indicates that use of a paired t-test is reasonable. Perform the hypothesis test by using eitherthe critical-value approach or the P-value approach as indicated. Assume that the null hypothesis is  $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-Five students took a math test before and after tutoring. Their scores were as follows. $$\begin{array} { c | r r r r r }  \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \ \hline \text { Before } & 66 & 73 & 71 & 66 & 75 \ \hline \text { After } & 70 & 82 & 69 & 69 & 87 \end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the mean score before tutoring differs from the mean score after tutoring? Use the critical-value approach.

Accepted Answer

The answer of Preliminary data analyses indicates that use of...

Question 15

Perform the required hypothesis test by using a Mann-Whitney test. Use a normal approximation for M. Find the meanand standard deviation of M, the value of M and of the test statistic, the critical value(s), and state your conclusion.
-Test whether the mean grade for students from college A differs from the mean grade for students from College B. Independent simple random samples of 11 students from College A and 11 students from College B are selected. Grades of the students are shown in the table. Use a 0.05 level of significance. $$\begin{array} { l l l l l l l l l l l l }  \text { College A } & 3.2 & 4.0 & 2.4 & 2.6 & 2.0 & 1.8 & 1.3 & 0.0 & 0.5 & 1.4 & 2.9 \ \hline \text { College B } & 2.4 & 1.9 & 0.3 & 0.8 & 2.8 & 3.0 & 3.1 & 3.1 & 3.1 & 3.5 & 3.5 \end{array}$$

Accepted Answer

The answer of Perform the required hypothesis test by using...

Question 16

Preliminary data analyses indicates that use of a paired t-test is reasonable. Perform the hypothesis test by using eitherthe critical-value approach or the P-value approach as indicated. Assume that the null hypothesis is  $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-The table below shows the weights, in pounds, of seven subjects before and after following a particular diet for two months. $$\begin{array} { c | r r r r r r r }  \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } \ \hline \text { Before } & 196 & 187 & 177 & 161 & 197 & 168 & 154 \ \hline \text { After } & 189 & 178 & 175 & 166 & 183 & 170 & 142 \end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the diet is effective in reducing weight? Use the critical-value approach.

Accepted Answer

The answer of Preliminary data analyses indicates that use of...

Question 17

Preliminary data analyses indicate that you can reasonably use nonpooled t-procedures on the given data. Apply anonpooled t-test to perform the required hypothesis test, using either the critical-value approach or the P-value approachas indicated.
-A paint manufacturer wished to compare the drying times of two different types of paint. Independent simple random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. $$\begin{array} { r | r } 
\ { \text { Type A } } & \text { Type B } \
\hline\bar{{ x}  _ { 1 }} = 74.7 & \bar{ { x } _ { 2 } }= 64.4 \
\mathrm {~s} _ { 1 } = 4.5 & \mathrm {~s} _ { 2 } = 5.1 \
\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 9
\end{array}$$ At the 1% significance level, do the data provide sufficient evidence to conclude that the mean drying time for type A differs from the mean drying time for type B? Use the critical-value approach.

Accepted Answer

The answer of Preliminary data analyses indicate that you can...

Question 18

Preliminary data analyses indicate that you can reasonably use nonpooled t-procedures on the given data. Apply anonpooled t-test to perform the required hypothesis test, using either the critical-value approach or the P-value approachas indicated.
-A researcher was interested in comparing the response times of two different cab companies. Companies A and B were each called at 50 randomly selected times. The calls to company A were made independently of the calls to company B. The response times for each call were recorded. The summary statistics were as follows: $$\begin{array} { l l l }  & \text { Company A } & \text { Company B } \ \hline \text { Mean response time } & 7.6 \text { minutes } & 6.9 \text { minutes } \ \text { Standard deviation } & 1.4 \text { minutes } & 1.7 \text { minutes } \end{array}$$ At the 0.02 level of significance, do the data provide sufficient evidence to conclude that the mean response time for company A differs from the mean response time for company B? Use the P-value approach.

Accepted Answer

The answer of Preliminary data analyses indicate that you can...

Question 19

Suppose that you want to perform a hypothesis test based on independent simple random samples to compare the means of two populations. Further suppose that the variable under consideration is normally distributed on each of the two populations and that the population standard deviations are unknown. If the sample standard deviations are 3.8 and 6.1, respectively, and the sample sizes are 25 and 60, respectively, would you use the pooled or the nonpooled t-test? Explain your answer.

Accepted Answer

The answer of Suppose that you want to perform a...

Question 20

Suppose that you want to perform a hypothesis test to compare the means of two populations. Several procedures are available, namely, the pooled t-test, the nonpooled t-test, the Mann-Whitney test, the paired t-test, and the Wilcoxon signed-rank test. Before selecting the appropriate procedure, you need to look at the sample data to ascertain distribution type. What methods are available for doing this?

Accepted Answer

The answer of Suppose that you want to perform a...

Quiz 10: Inferences for Two Population Means

Suppose that you want to perform a hypothesis test to compare the means of two populations using paired samples. How would you decide between the paired t-test and the paired Wilcoxon signed-rank test?

Suppose that you want to perform a hypothesis test to compare the means of two populations using independent simple random samples. The two distributions of the variable under consideration have the same shape. How would you decide between the pooled t-test and the Mann-Whitney test?

The pooled t-test requires the assumption that the two population standard deviations be equal. What methods are available for checking this assumption? Which of these methods is not recommended and why is it not recommended?