Suppose we wish to test the null hypothesis that there is no association between

Question

Suppose we wish to test the null hypothesis that there is no association between year in school and opinion. Under the null hypothesis, what is the expected number of strongly opposed seniors?

Recent revenue shortfalls in a Midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25% tuition increase. It was determined that such an increase was needed to simply compensate for the lost support from the state. Random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether or not they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are given in the following table. Year in school Opinion Freshman Sophomore Junior Senior Strongly opposed 39 36 29 18 Not strongly opposed 11 14 21 32

Suppose we wish to test the null hypothesis that there is no association between year in school and opinion. Under the null hypothesis, what is the expected number of strongly opposed seniors?

Explanation / Answer

H0: there is no association between year in school and opinion.

Ha: there is association between year in school and opinion.

Chi square test

              Opinion          Freshman       Sophomore        Junior         Senior         Total

Strongly opposed           39(30.50)       36(30.50)           29(30.50) 18(30.50)       122

Not strongly opposed      11(19.50)       14(19.50)       21(19.50)    32(19.50)      78

Total                                50                   50                    50             50            200(Grand total)

Bracketed frequencies are expected frequencies calculated as row total*column total/Grand total.

For example, expected value for strongly opposed senior is 122*50/200 = 30.50.

Same calculation for expected frequency for all entries.

Expected number of strongly opposed senior are 30.50.

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