Grade The contingency table shows how a random sample of college freshmen graded

Question

Grade The contingency table shows how a random sample of college freshmen graded the leaders of three types of institutions. At a 0.01, can you conclude that the grades are related to the institution? Complete parts (a) through (d) Institution Military Religious Media/Press D/F 25 12 28 40 17 48 22 20 39 174818 D (a) Identify the claim and state the null and alternative hypotheses Ho: Grades are (1) Ha Grades are (2) The (3) (b) Determine the degrees of freedom, find the critical value, and identify the rejection region What are the degrees of freedom? the institution the institution. is the claim Find the critical value (Round to three decimal places as needed.) Choose the correct rejection region below (c) Calculate the test statistic. If convenient, use technology x2 (Round to three decimal places as needed.) (d) Decide to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim Choose the correct conclusion below. O A. Fail to reject the null hypothesis. There is O B. Reject the null hypothesis. There is enough enough evidence to conclude that grades are dependent on the institution evidence to conclude that grades are dependent on the institution. ° C. Reject the null hypothesis. There is not enough evidence to conclude that grades are dependent on the institution. D. Fail to reject the null hypothesis. There is not enough evidence to conclude that grades are dependent on the institution. (1) O independent of (2) O dependent on(3) O null hypothesis O dependent on O independent of alternative hypothesis

Explanation / Answer

The statistical software output for this problem is:

Contingency table results:
Rows: var4
Columns: None

Chi-Square test:

Hence,

a) Ho: Independent

Ha: Dependent

alternative hypothesis

b) D.f. = 6

Critical value = 16.812

Rejection region: Option C is correct.

c) Test statistic = 39.410

d) Option B is correct.

A B C D/F Total Military 40 41 18 25 124 Religious 17 48 22 12 99 Media/ Press 17 20 39 28 104 Total 74 109 79 65 327

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