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 σ 2 of lifetimes of these batteries...


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 limitmonths
upper limitmonths



Jun 01, 2022
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