The following problem is based on information taken from Academe, Bulletin of the American Association of University Professors. Let x represent 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 of x is approximately s² = 47.1. However, a random sample of 15 colleges and universities in Kansas showed that x has a sample variance s² = 83.2. 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.

Please provide the following information.

(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. What are the degrees of freedom? What assumptions are you making about the original distribution?

(c) Find or estimate the P-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 of independence?

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

(f) Find the requested confi­dence interval for the population variance or population standard deviation. Interpret the results in the context of the application.