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Let x represent the average annual salary of collegeand university professors (in thousands of dollars) in the UnitedStates. For all colleges and universities in the United States, thepopulation variance of x is approximatelyσ² = 47.1. However, a random sample of 15colleges and universities in Kansas showed that x has asample variance s² = 85.4. Use a 5% level ofsignificance to test the claim that the variance for colleges anduniversities in Kansas is greater than 47.1. Find a 95% confidenceinterval for the population variance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 47.1;H₁: σ² < 47.1H_o: σ² < 47.1;H₁: σ² =47.1     H_o:σ² = 47.1; H₁:σ² ≠ 47.1 H_o:σ² = 47.1; H₁:σ² > 47.1

(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 originaldistribution?

We assume a exponential population distribution. We assume abinomial population distribution.     We assumea normal population distribution. We assume a uniform populationdistribution.

(c) Find or estimate the P-value of the sample teststatistic.

P-value > 0.100 0.050 < P-value <0.100     0.025 < P-value <0.050 0.010 < P-value < 0.025 0.005 <P-value < 0.010 P-value < 0.005

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

Since the P-value > α, we fail to rejectthe null hypothesis. Since the P-value > α, wereject the null hypothesis.     Since theP-value ≤ α, we reject the null hypothesis. Sincethe P-value ≤ α, we fail to reject the nullhypothesis.

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

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

(f) Find the requested confidence interval for the populationvariance. (Round your answers to two decimal places.)

lower limit
upper limit   Â

Interpret the results in the context of the application.

We are 95% confident that σ² lies withinthis interval. We are 95% confident that σ²lies above this interval.     We are 95%confident that σ² lies outside this interval.We are 95% confident that σ² lies below thisinterval.