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 = 79.8. 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. Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? (e) Interpret your conclusion in the context of the application. At the 5% level of significance, there is insufficient evidence to conclude the variance of annual salaries is greater in Kansas.At the 5% level of significance, there is sufficient evidence to conclude the variance of annual salaries is greater in Kansas. (f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.) lower limit upper limit Interpret the results in the context of the application. We are 95% confident that σ2 lies above this interval.We are 95% confident that σ2 lies within this interval. We are 95% confident that σ2 lies outside this interval.We are 95% confident that σ2 lies below this interval.
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 = 79.8. 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. Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? (e) Interpret your conclusion in the context of the application. At the 5% level of significance, there is insufficient evidence to conclude the variance of annual salaries is greater in Kansas.At the 5% level of significance, there is sufficient evidence to conclude the variance of annual salaries is greater in Kansas. (f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.) lower limit upper limit Interpret the results in the context of the application. We are 95% confident that σ2 lies above this interval.We are 95% confident that σ2 lies within this interval. We are 95% confident that σ2 lies outside this interval.We are 95% confident that σ2 lies below this interval.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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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 = 79.8. 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.
Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
What are the degrees of freedom?
(e) Interpret your conclusion in the context of the application.
At the 5% level of significance, there is insufficient evidence to conclude the variance of annual salaries is greater in Kansas.At the 5% level of significance, there is sufficient evidence to conclude the variance of annual salaries is greater in Kansas.
(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)
| lower limit | |
| upper limit |
Interpret the results in the context of the application.
We are 95% confident that σ2 lies above this interval.We are 95% confident that σ2 lies within this interval. We are 95% confident that σ2 lies outside this interval.We are 95% confident that σ2 lies below this interval.
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