The personality study discussed earlier in this chapter not only compared the distribution of four types (Alpha, Beta, Gamma, Delta) in a sample of 588 college students with a sample of college students classified during the 1980s but also compared it with a sample of 147 graduate students, saying that "we reasoned that graduate students would differ from typical undergraduates on personality characteristics that support academic achievement" (Stewart \& Bernhardt, 2010, p. 582). The following contingency table shows the distribution of the types for the college students and the graduate students:

Conduct the chi-square test of independence to address whether the distribution of the four types depends on the type of student (college student vs. graduate student).

a. Draw a bar chart of the data.

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

c. Make a decision about the null hypothesis.
(1) Calculate the degrees of freedom \((d f)\).
(2) Set alpha ( \(\alpha\) ), identify the critical value, and state a decision rule.
(3) Calculate a statistic: chi-square \(\left(\chi^{2}\right)\).
(4) Make a decision whether to reject the null hypothesis.
(5) Determine the level of significance.
(6) Calculate a measure of effect size (Cramér's \(\phi\) ).

d. Draw a conclusion from the analysis.

Exercise 11

"Sex in advertising prompts much discussion and media attention, typically how advertisers blend sex with their brands to gain attention" (Reichert \& Lambiase, 2003, p. 120). As part of their study, they asked the following question: "Are sexual ads more likely to appear in women's or men's magazines?" (p. 125). To address this question, they examined the full-page advertisements in a sample of women's and men's magazines and found 107 sexual ads that were divided into women's and men's magazines as follows:

To determine whether sexual ads were more likely to be found in women's or men's magazines, conduct the chi-square goodness-of-fit test (assume equal proportions):

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Type Alpha Beta Gamma Delta Total: College 251 65 194 78 588 Type of Student 42.7% 11.0% 33.0% 13.3% 100.0% Graduate 88 16 35 8 147 59.9% 10.9% 23.8% 5.4% 100.0% Total 339 81 229 86 735