1. For the following problem, state the most likely hypothesis and compute a repeated-measures ANOVA to determine whether a statistically significant difference exists between the groups in question. Use an \(\alpha\) -Level of 0.05. Perform the computations for the problem both by hand and using statistical software. Note that this example may not meet all the assumptions for the repeated-measures ANOVA.

- Problem: A physical therapist wants to know which of three exercise machines increases heart rate the most. She recruits a group of cardiac rehabilitation patients into her study. The participants heart rates are recorded after they use three types of exercise equipment for 10 minutes. Each piece of equipment is tried on a different visit, and the order of use is randomized for each person. Is there a difference between the three pieces of exercise equipment in terms of the effect on heart rate?

1. State the null and alternative hypotheses.
2. Using \(\alpha=0.05\), determine the degrees of freedom and identify the critical value.
3. Compute the mean and standard deviation for each group (software can be used).
4. Perform a repeated-measures ANOVA and complete the repeated measures ANOVA table.
   Perform a modified Bonferroni \(t\) test to determine which means are significantly different from each other, if applicable.
5. Determine statistical significance and clearly state a conclusion.
6. Upload your statistical software results and provide a concise summary of the various output measures and conclusions of the test.

2. For the following problem, state the most likely hypothesis and compute a Friedman's ANOVA by rank to determine whether a statistically significant difference exists between the groups in question. Use an \(\alpha\) -Level of 0.05. Perform the computations for the problem both by hand and using statistical software.

- Problem: An instructor wants to know whether taking the statistics series improved students' inherent math abilities as measured by a 100 -point assessment. Students complete the assessment before they take the first statistics course, after they take the basic course, and again after they take the advanced math course. The scores are shown in the following table. What should the instructor conclude?

1. State the null and alternative hypotheses.
2. Using \(\alpha=0.05\) identify the critical value for the \(f\) test.
3. Compute the median and interquartile range for each group (software can be used).
4. Compute Friedman's ANOVA by rank statistic.
   Perform a modified Student-Newman-Keuls post hoc test if necessary.
5. Determine statistical significance and clearly state a conclusion.
6. Upload your statistical software results and provide a concise summary of the various output measures and conclusions of the test.

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Solution: The downloadable solution consists of 18 pages, 1367 words and 3 charts.
Deliverable: Word Document