Question

A group of 15 swimmers is chosen to participate in an experiment to see if a new breathing style will improve their stamina. Each swimmer's pulse recovery rate is measured after a 20 minute workout using the old breathing style. The swimmers practice the new style for two weeks, and then measure their pulse recovery rates after a 20 minute workout using the new style. They will continue to use the new breathing style if it is shown to reduce pulse recovery time. Let un represent the population mean pulse recovery rate when using the old breathing style. Let uz represent the population mean pulse recovery rate when using the new breathing style. Let D; denote the difference in recovery rates between the old and new styles, and let D and s denote the sample mean and standard deviation, respectively, of these differences. Describe the appropriate test. State the appropriate null and alternate hypotheses, describe the test statistic, and specify which table should be used to find the P-value. If relevant, state the number of degrees of freedom for the test statistic. Check all that are true. Check All That Apply A test for the difference between two means is appropriate. The appropriate null and alternate hypotheses are Ho: 11-02 0 versus Hy: 41-42 <0. The test statistic is D/ (s//20). The z table should be used to find the P-value. There are 19 degrees of freedom. The data are paired, so this requires a paired test for the mean difference.

Answer 1

This is a paired t test problem.

A paired t-test is used when we are interested in the difference between two variables for the same subject.

Correct options are:

A TEST FOR THE DIFFERENCE BETWEEN TWO MEANS IS APPROPRIATE.

THE DATA ARE PAIRED, SO THIS REQUIRES A PAIRED TEST FOR THE MEAN DIFFERENCE.

THE APPROPRIATE NULL AND ALTERNATE HYPOTHESES ARE H0:$\mu1-\mu2\leq0$ versus H1:$\mu1-\mu2>0$

THE TEST STATISTIC IS $\bar{D} /s/\sqrt{15}$ ​​​​​​. THE t TABKE SHOULD BE USED TO FIND THE P VALUE.​​​​​​

THERE ARE 14 DEGREES OF FREEDOM.