Question

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 σ² = 47.1. However, a random sample of 19 colleges and universities in Kansas showed that x has a sample variance s² = 82.6. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1.

(A) What is the level of significance?

(B) State the null and alternate hypotheses.

H₀: σ² = 47.1; H₁: σ² < 47.1

H₀: σ² = 47.1; H₁: σ² > 47.1    

H₀: σ² < 47.1; H₁: σ² = 47.1

H₀: σ² > 47.1; H₁: σ² = 47.1

H₀: σ² = 47.1; H₁: σ² ≠ 47.1

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

(D) What are the degrees of freedom?

(E) What assumptions are you making about the original distribution?

We assume a binomial population distribution.

We assume a uniform population distribution.    

We make no distributional assumptions.

We assume a exponential population distribution.

We assume a normal population distribution.

(F) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)

(G) Based on your answers in parts (a) to (f), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

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

At the 5% level of significance, there is sufficient evidence to conclude the variance of annual salaries is greater in Kansas.

At the 5% level of significance, there is insufficient evidence to conclude the variance of annual salaries is greater in Kansas.    

Answer 1