In 2011, the student body of a state university in Alabama consists of 30% freshmen, 25% sophomores, 27% juniors, and 18% seniors. A sample of 400 students taken from the 2012 student body showed that there are 138 freshmen, 88 sophomores, 94 juniors, and 80 seniors. Test with 5% significance level to determine whether the student body proportions have changed
H0: p1 = .30, p2 =.25, p3 = 0.27, p4 = .18
H1: At least one proportion differs from their specified values
Rejection region: ?2 > ?2.05,3 = 7.815
Test statistic: ?2 = 6.844
Conclusion: Cannot reject the null hypothesis. The student body proportions have not changed since 2011, according to the data.
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