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, however it is included to start you off with a problem that is easy to compute.

- Problem: A pilot study is conducted to measure the effectiveness of four different techniques for reducing test anxiety in students. Each student tries a different technique before taking an examination (spaced 3 weeks apart), and the order that the techniques were used is randomly assigned to each student . Anxiety is measured by a scale that generates sum scores ranging from 0 to 20 , with 0 indicating the least anxiety and 20 indicating the most anxiety. Which technique appears to work the best?

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: 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 \(\alpha=0.05\) 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.

Price: $20.53

Solution: The downloadable solution consists of 13 pages, 753 words and 2 charts.
Deliverable: Word Document