A teacher hypothesizes there is a positive relationship between her students' scores on a midterm examination and on the final examination.

a. Draw a scatterplot of the data.

b. Calculate descriptive statistics (the mean and standard deviation) for the two variables.

c. State the null and alternative hypotheses \(\left(\mathrm{H}_{0}\right.\) and \(\left.\mathrm{H}_{1}\right)\) (use a nondirectional \(\left.\mathrm{H}_{1}\right)\).

d. Make a decision about the null hypothesis.
(1) Calculate the degrees of freedom \((d f)\).
(2) Set alpha \((\alpha)\), identify the critical values, and state a decision rule.
(3) Calculate a statistic: Pearson correlation ( \(r\) ).
(4) Make a decision whether to reject the null hypothesis.
(5) Determine the level of significance.
(6) Calculate a measure of effect size \(\left(r^{2}\right)\).

e. Draw a conclusion from the analysis.

f. Relate the result of the analysis to the research hypothesis.

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