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 = 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) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) B) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.) lower limit upper limit C) Interpret the results in the context of the application.
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 = 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) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
B) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)
| lower limit | |
| upper limit |
C) Interpret the results in the context of the application.
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