Aa Aa 14. The chi-square test for independence A social psychologist is interest

Question

Aa Aa 14. The chi-square test for independence A social psychologist is interested in finding out whether people who self-identify as introverted 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 introverted. The following frequency distribution table summarizes the responses to the two survey questions. College Type Agricultural, Technical, or Liberal Arts 4-Year Community or Total 910 346 1,256 College University Junior College Specialized College Other 255 125 Total 259 [ 457 380 346 82 48 130 Extroverted 218 Introverted 41 21 30 The following questions walk you through the steps of a test of the nul hypothesis that a student's choice of college type is independent of whether he self-identifies as introverted. 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 introverted, then t frequency for the Extroverted/4-Year University category is he expected When you calculate the chi-square test statistic, you add up the contributions from each of the 10 categories. E contribution consists of the squared difference between the expected nd observed frequences category, divided b red difference between the expected and observed trequencies for that particulasr Y the expected frequency-that is, (fo- 2/ te. The contribution of the Extroverted/4-Year

Explanation / Answer

SOLUTION

a) 3 missing values:

4-year University column total = 457; Extroverted row total = 830; Grand total = 1156

b) Expected frequency for Extroverted/4-year University = (457 x 830)/1156 = 328.123

c) Contribution of the above to 2 = (346 – 328.123)2/328.123 = 0.974

d) Total 2 = 57.838 + 0.172 = 58.812

e) Critical value = upper 1% point of 26 = 16.81[from standard 2 table. Can also be found using Excel Function ]

f) Reject H0 if 2 16.81

g) Since 2 (58.812) > 16.81, H0 is rejected.

DONE

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