Letxrepresent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance ofxis approximately²= 47.1. However, a random sample of20colleges and universities in Kansas showed thatxhas a sample variances²=80.5. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Find a 95% confidence interval for the population variance.

(a) What is the level of significance?

State the null and alternate hypotheses.

(b)Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)

What are the degrees of freedom?

What assumptions are you making about the original distribution?

(c)Find or estimate theP-value of the sample test statistic.

(d)Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

(e)Interpret your conclusion in the context of the application.