Question 1

Determine the null and alternative hypotheses for the proposed hypothesis test.
-A company which designs sports shoes has made an improvement to their popular running shoe. They hope that athletes wearing the new running shoe will be able to run faster over short Distances. They will use a paired sample to determine whether the mean time to run 100 meters for Sprinters wearing the new running shoe is less than the mean time to run the 100 meters for
Sprinters wearing the old running shoe.

Accepted Answer

The null hypothesis always states that there is no effect or no difference, so it should state that the mean times are equal ($\mu_1 = \mu_2$). The alternative hypothesis reflects the research hypothesis that the new shoe improves speed, thus the mean time with the new shoe ($\mu_1$) is less than with the old shoe ($\mu_2$).

Question 2

Suppose that x is a normally distributed variable on each of two populations. Independent samples of sizes n₁ and n₂, respectively, are selected from the two populations. The mean of all possible Differences between the two sample means is equal to which of the following?

Accepted Answer

The mean of all possible differences between two sample means is equal to the difference between the two population means. This is a property of the sampling distribution of the difference between two means.

Question 3

Preliminary data analyses indicates that use of a paired Wilcoxon signed-rank test is reasonable. Perform the hypothesistest by using a paired Wilcoxon signed-rank test. Assume that the null hypothesis is $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-Students are given scores on both the mathematics section and the verbal section of a standardized test. The data for a random sample of students is given below. $\begin{array} { l l l l l l l l l l }  \text { Mathematics } & 347 & 440 & 327 & 456 & 427 & 349 & 377 & 398 & 425 \ \hline \text { Verbal } & 285 & 378 & 243 & 371 & 340 & 271 & 294 & 322 & 385 \end{array}$ At the 5% significance level, do the data provide sufficient evidence to conclude that there is a difference between the mean math score and the mean verbal score?

Accepted Answer

$\begin{array} { l }  \mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \ \mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } \neq \mu _ { 2 } \ \alpha = 0.05 \ \mathrm {~W} = 45 \end{array}$ 
Critical values $= 6$ and 39 Reject $\mathrm { H } _ { 0 }$. At the $5 \%$ significance level, the data provide sufficient evidence to conclude that there is a difference between the mean math score and the mean verbal score.

Question 4

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.
-A person who commutes to work is choosing between two different routes. He tries the first route 11 times and the second route 12 times and records the time of each trip. The results (in minutes)are shown below. Use a significance level of 0.01 to test whether the mean time for route 1 differs from the mean time for route 2.

Accepted Answer

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

Question 5

Which of the following statements regarding the equal-standard-deviations assumption of the pooled t-test is the most accurate?

Accepted Answer

The pooled t-test assumes that the two populations have equal variances (homogeneity of variances). It is robust to moderate violations of this assumption if the sample sizes of the two groups are roughly equal, because the impact of unequal variances is minimized when the groups are of similar size.

Question 6

Determine the null and alternative hypotheses for the proposed hypothesis test.
-A pharmaceutical company wants to determine whether its new antianxiety medication has any effect on resting pulse rate. They will use a paired sample to determine whether the mean resting
Pulse rate for adults not taking the antianxiety medication differs from the mean resting pulse rate
For adults who are taking the antianxiety medication.

Accepted Answer

The correct hypothesis setup for testing if there is any effect (either increase or decrease) on the resting pulse rate due to the antianxiety medication is to have a null hypothesis stating there is no difference ($\mu_1 = \mu_2$) and an alternative hypothesis stating there is a difference ($\mu_1 \neq \mu_2$). This is a two-tailed test appropriate for detecting any effect.

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 amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows. 
$\begin{array} { r | r }  \text { Women } & \text { Men } \ \hline \mathrm { x } _ { 1 } = 12.6 & \mathrm { x } _ { 2 } = 14.1 \ \mathrm {~s} _ { 1 } = 3.9 & \mathrm {~s} _ { 2 } = 5.2 \ \mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 17 \end{array}$  
At the 5% significance level, do the data provide sufficient evidence to conclude that the mean amount of time spent watching television by women is less than the mean amount of time spent watching television by men? Use the critical-value approach.

Accepted Answer

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

Question 8

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 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 9

Determine the null and alternative hypotheses for the proposed hypothesis test.
-A researcher wants to use a paired sample to determine whether the mean number of hours spent exercising per week for married men differs from the mean number of hours spent exercising per Week for married women.

Accepted Answer

The null hypothesis always specifies a statement of equality (e.g., $\mu_1 = \mu_2$), and the alternative hypothesis specifies the research hypothesis of interest, which in this case is that there is a difference ($\mu_1 \neq \mu_2$).

Question 10

Determine the null and alternative hypotheses for the proposed hypothesis test.
-The forced vital capacity (FVC)is often used by physicians to assess a person's ability to move air in and out of their lungs. It is the maximum amount of air that can be exhaled after a deep breath. A Researcher wants to perform a hypothesis test to determine whether the mean forced vital capacity For adults who are smokers is less than the mean forced vital capacity for adults who are former Smokers. He will use a paired sample to determine whether forced vital capacity increases, on Average, when adults stop smoking.

Accepted Answer

The null hypothesis typically states that there is no effect or no difference, so it should state that the means are equal ($\mu_1 = \mu_2$). The alternative hypothesis reflects the research hypothesis that the mean forced vital capacity for smokers is less than for former smokers ($\mu_1 < \mu_2$).

Question 11

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  $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$
-A coach uses a new technique in training middle distance runners. The times, in seconds, for 8 different athletes to run 800 meters before and after this training are shown below. $$\begin{array} { r | r r r r r r r r }  \text { Athlete } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } \ \hline \text { Before } & 109.7 & 112.3 & 109.5 & 118.3 & 111.1 & 120 & 117.1 & 114.6 \ \hline \text { After } & 110.3 & 111 & 107.1 & 119.1 & 109.3 & 120.1 & 113.5 & 110.7 \end{array}$$ At the 5% significance level, do the data provide sufficient evidence that the training helps to improve times for the 800 meters? Use the critical-value approach.

Accepted Answer

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

Question 12

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 salaries of female and male employees at a particular company. Independent simple random samples of 8 female employees and 15 male employees yielded the following weekly salaries (in dollars).  
$\begin{array}{r|rr} \text { Female } & \text { Male } & \ \hline 495 & 722 & 518 \ 760 & 562 & 904 \ 556 & 880 & 1150 \ 904 & 520 & 805 \ 520 & 500 & 480 \ 1005 & 1250 & 970 \ 743 & 750 & 605 \end{array}$  
At the $5 \%$ significance level, do the data provide sufficient evidence to conclude that at this company the mean salary of female employees is less than the mean salary of male employees? Use the critical-value approach. (Note: $\bar { x } _ { 1 } = 705.375 , \bar { x } _ { 2 } = 817.067 , \mathrm {~s} _ { 1 } = 183.855 , \mathrm {~s} _ { 2 } = 330.146 .$

Accepted Answer

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

Question 13

A teacher is interested in performing a hypothesis test to compare the mean math score of the girls and the mean math score of the boys. She randomly selects 10 girls from the class and then randomly selects 10 boys. She arranges the girls' names alphabetically and uses this list to assign each girl a number between 1 and 10. She does the same thing for the boys. She pairs each girl with the boy having the same number. She then performs a paired t-test. Do you think that in this situation a paired t-test is appropriate? Explain your answer.

Accepted Answer

The answer of A teacher is interested in performing a...

Question 14

Determine the null and alternative hypotheses for the proposed hypothesis test.
-A nutritionist wants to investigate whether her new diet will be effective in helping women aged 30-40 to lose weight. She will use a paired sample to determine whether the mean weight of Women before going on this diet is greater than the mean weight of women after being on this diet For two months.

Accepted Answer

The null hypothesis always states that there is no effect or no difference, so it should state that the mean weights before and after the diet are equal ($\mu _ { 1 } = \mu _ { 2 }$). The alternative hypothesis reflects the research hypothesis that the diet will cause a decrease in weight, thus $\mu _ { 1 } > \mu _ { 2 }$.

Question 15

A researcher would like to conduct a hypothesis test to compare the mean SAT scores of students who have received extra coaching and the mean test score of students who have not received extra Coaching. He will randomly select 15 students and will use the difference between the student's
Score after coaching and the student's score before coaching as the paired-difference variable. He Obtains some normal probability plots of the sample data to determine whether it would be Reasonable to use a paired t-test. In which of the following situations would it be reasonable to use
A paired t-test ?
A: The distribution of the before test scores appears normal, the distribution of the after test scores
Appears normal, however the distribution of the paired differences does not appear normal.
B: The distribution of the before test scores is nonnormal, the distribution of the after test scores is
Nonnormal, however the distribution of the paired differences appears normal.

Accepted Answer

B)B onlyFor a paired t-test, the normality assumption applies to the distribution of the paired differences, not the distributions of the individual groups before and after the intervention. Therefore, it is reasonable to use a paired t-test when the distribution of the paired differences appears normal, even if the individual scores before and after coaching are not normally distributed.

Question 16

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.
-Independent simple random samples of 11 female employees and 11 male employees are selected from one company and the weekly salaries of the employees are recorded. The salaries (in dollars)are shown below. Use a significance level of 0.10 to test whether the mean salary for female employees differs from the mean salary for male employees.

Accepted Answer

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

Question 17

Preliminary data analyses indicate that you can reasonably consider the assumptions for using the Mann-Whitney testsatisfied. Assume that the null hypothesis is $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$ . Use the Mann-Whitney test to carry out the requiredhypothesis test.
-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 9 students from college B yielded the following GPAs.  $\begin{array} { r | r }  \text { College A College B } \ \hline 2.8 & 3.6 \ 3.2 & 3.9 \ 3.7 & 3.3 \ 2.5 & 4.0 \ 2.6 & 3.8 \ 3.0 & 2.9 \ 4.0 & 3.6 \ 2.7 & 4.0 \ & 3.5 \end{array}$  
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?

Accepted Answer

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

Question 18

Suppose that you want to perform a hypothesis test to compare the means of two populations using independent simple random samples. In which of the situations below is it reasonable to use The Mann-Whitney test?

Accepted Answer

The Mann-Whitney test is a non-parametric test used when the assumptions of normality are not met but is most reliable when the distributions have the same shape.

Question 19

Provide an appropriate response.
-Suppose that $x$ is a normally distributed variable on each of two populations. Independent samples of sizes $n _ { 1 }$ and $n _ { 2 }$, respectively, are selected from the two populations. Explain the difference between $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ and $\mu _ { 1 } - \mu _ { 2 }$.

Accepted Answer

The answer of Provide an appropriate response.
-Suppose that $x$ is...

Question 20

Suppose that you want to perform a hypothesis test based on independent simple random samples to compare the means of two populations. Normal probability plots for the two samples are linear and therefore suggest that the variable under consideration is normally distributed on each population. Is it then reasonable to proceed with a pooled t-test? If not, what additional information is required and what methods might be used to obtain this information?

Accepted Answer

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

Quiz 10: Inferences for Two Population Means

Suppose that x is a normally distributed variable on each of two populations. Independent samples of sizes n1 and n2, respectively, are selected from the two populations. The mean of all possible Differences between the two sample means is equal to which of the following?

Which of the following statements regarding the equal-standard-deviations assumption of the pooled t-test is the most accurate?

Determine the null and alternative hypotheses for the proposed hypothesis test. -A researcher wants to use a paired sample to determine whether the mean number of hours spent exercising per week for married men differs from the mean number of hours spent exercising per Week for married women.

Suppose that you want to perform a hypothesis test to compare the means of two populations using independent simple random samples. In which of the situations below is it reasonable to use The Mann-Whitney test?

Suppose that x is a normally distributed variable on each of two populations. Independent samples of sizes n₁ and n₂, respectively, are selected from the two populations. The mean of all possible Differences between the two sample means is equal to which of the following?