Aa Aa E 4. The chi-square test for independence A social psychologist is interes

Question

Aa Aa E 4. The chi-square test for independence A social psychologist is interested in finding out whether people who self-identify as shy are more likely to attend certain types of colleges. He surveys college-bound graduating seniors and asks them what type of college they plan to attend and whether or not they consider themselves shy. The following frequency distribution table summarizes the responses to the two survey questions. College Type Agricultural, 4-Year Community or Technical, or Liberal Arts College University Junior College Specialized College other Total Not Shy 155 82 582 18 910 Shy 35 24 239 41 Total 179 89 821 59 The following questions walk you through the steps of a test of the null hypothesis that a student's choice of college type is independent of whether he self-identifies as shy. Fill in the three missing values in the frequency distribution table. If a student's choice of college type is independent of whether he self-identifies as shy, then the expected frequency for the Shy/Liberal Arts College category is When you calculate the chi-square test statistic, you add up the contributions from each of the 10 categories. Each contribution consists of the squared difference between the expected and observed frequencies for that particular category, divided by the expected frequency-that is, (fo fe)2 fe. The contribution of the Shy/Liberal Arts College category is

Explanation / Answer

from above

expected frequency for shy/liberal arts college category =29.752

contribution of shy/liberal arts college category = 0.926

X2 =89.4945

reject the null hypothesis if X2>=7.7794

weather a student a shy or not shy is rejected

Observed O liberal art 4 yr community agril other Total not shy 73 155 82 582 18 910 shy 35 24 7 239 41 346 Total 108 179 89 821 59 1256 Expected E=rowtotal*column total/grand total liberal art 4 yr community agril other Total not shy 78.248 129.689 64.482 594.833 42.747 910 shy 29.752 49.311 24.518 226.167 16.253 346 Total 108 179 89 821 59 1256 chi square =(O-E)^2/E liberal art 4 yr community agril other Total not shy 0.352 4.9397 4.7589 0.2769 14.3263 24.654 shy 0.926 12.992 12.516 0.728 37.679 64.841 Total 1.278 17.931 17.275 1.005 52.005 89.4945

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.