1. For the following problem, state the most likely hypothesis and compute an ANCOVA test. Use an \(\alpha\) -Level of 0.05. Perform the computations for the problem using statistical software.

- Problem: A researcher wished to make a preliminary determination regarding which of the four novel methods of teaching reading available to a school district might be more effective for third-grade students. The researcher randomly selected 24 third-grade students and then randomly assigned 6 of them to each of the four methods of reading instruction. After several months of reading instruction, a posttest was administered. Conduct an ANCOVA to assess whether the posttest scores differ by teaching method when taking the pretest score into account, i.e. controlling pretest score influence.

1. State the null and alternative hypotheses.
2. Make sure that the data meet all the necessary assumptions, e.g. examine the correlation between the covariate and the dependent variable, see whether there is an interaction effect, check to make sure there is homogeneity of variance, etc.
3. Compute the mean and adjusted mean for each group.
4. Examine the ANCOVA Table.
5. Determine statistical significance and clearly state a conclusion.

2. For the following problem, state the most likely hypothesis and compute a Pearson correlation coefficient. Use an \(\alpha\) -Level of 0.05 (two-tailed). Perform the computations for the problem both by hand and using statistical software.

- Problem: An HMO administrator wants to examine the relationship of self-rated health to the number of physician visits made in 1 year. The self-rated health is rated on a scale of 1 to 5 , where 1= poor health and 5= excellent health; the number of physician visits made in the past year is shown in the table below:

1. State the null and alternative hypotheses.
2. Using \(\alpha=0.05\) (two-tailed) obtain the critical value for \(r\).
3. Check to make sure that the data meet all of the necessary assumptions (include scatter plot).
4. Perform the computations necessary to obtain a Pearson correlation coefficient.
5. Determine statistical significance and clearly state a conclusion.

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