Chapter 11, Problem 7CR

Before you solve Problems 6-10, first classify the problem as one of the following:

Chi-square test of independence or homogeneity

Chi-square goodness of fit

Chi-square for testing ${\sigma }^2\text{ or }\sigma$

Then in each of the problems when a test is to be performed do the following:

(i) Give the value of the level of significance. State the null and alternate hypotheses.

(ii) Find the sample test statistic.

(iii) Find or estimate the P-value of the sample test statistic.

(iv) Conclude the test.

(v) Interpret the conclusion in the context of the application.

Teacher Ratings: Grades Professor Stone complains that student teacher ratings depend on the grade the student receives. In other words, according to Professor Stone, a teacher who gives good grades gets good ratings, and a teacher who goes had grades gets had ratings. To test this claim, the Student Assembly took a random sample of 300 teacher ratings on which the student's grade fur the course also was indicated. The results are given in the following table. Test the hypothesis that teacher ratings and student grades are independent at the 0.01 level of significance.

Rating	A	B	c	f (or withdrawal)	Row Total
Excellent	14	18	15	3	50
Average	25	35	75	15	150
Poof	21	27	40	12	100
Column Total	60	80	110	30	300