Past research has examined relationships between people's backgrounds and their personality. For example, Eysenck (1982) found a relationship between blood type and introversion, and Pellegrini (1973) concluded that astrological signs were related to level of femininity. Gupta (1992) examined the relationship between season of birth and impulsivity (the lack of ability or desire to control one's behavior). Gupta hypothesized that people born in the seasons with more extreme temperatures (winter and summer) are more impulsive than those born in the more mild seasons (spring and autumn). She asked a sample of adults to report their season of birth and then administered a personality measure of impulsivity. Imagine the following descriptive statistics are reported for the test scores: Winter: \(N=6, M=8.31, s=1.74\); Spring: \(N\) = 6, \(M=6.52, s=1.87\); Summer: \(N=6, M=9.09, s=2.35\); Fall: \(N=6, M=5.86, s\) \(=1.95\).

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.