Although men and women have been found to perform differently on tests of mental ability, less is known about possible reasons for these differences. A researcher hypothesizes that one's beliefs play a role, such that women who believe they should not perform well on these tests as men will in fact not perform well. To test this hypothesis, a group of women are given a written test of spatial abilities. Three different instructions were included with this test: (1) Women perform better on the test than men, (2) men perform better on the test than women, or (3) women and men perform equally well on the test. It was hypothesized that women who were told that women perform better than men would score higher than women who were told men were better or that women and men were equal. Here are descriptive statistics of the test scores: Women better: \(N=11, M=6.91, s=2.63\); Men better: \(N=11, M=\) 7.45, \(s=2.07\); Women and men equal: \(N=11, M=9.82, s=2.23\).

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

b. Make a decision about the null hypothesis.
1, Calculate the degrees of freedom \((d f)\).
2, Set alpha (a), identify the critical value, and state a decision rule.
3, Calculate the \(F\)-ratio \((F)\) and create an ANOVA summary table.
4, Make a decision whether to reject the null hypothesis.
5, Determine the level of significance.
6, Calculate a measure of effect size \(\left(R^{2}\right)\).

c. Draw a conclusion from the analysis.

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