A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 22 batteries gave a sample variance of 13.2 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23. (a) What is the level of significance? Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? (f) Find a 90% confidence interval for the population variance. (Round your answers to two decimal places.) lower limit upper limit (g) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.) lower limit months upper limit months
A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 22 batteries gave a sample variance of 13.2 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23. (a) What is the level of significance? Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? (f) Find a 90% confidence interval for the population variance. (Round your answers to two decimal places.) lower limit upper limit (g) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.) lower limit months upper limit months
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ2 of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ2 = 23 months (squared) is most desirable for these batteries. A random sample of 22 batteries gave a sample variance of 13.2 months (squared). Using a 0.05 level of significance, test the claim that σ2 = 23 against the claim that σ2 is different from 23.
(a) What is the level of significance?
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 are the degrees of freedom?
(f) Find a 90% confidence interval for the population variance. (Round your answers to two decimal places.)
(g) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)
| lower limit | |
| upper limit |
(g) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)
| lower limit | months |
| upper limit | months |
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