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 variance²of 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 of²= 23 months (squared) is most desirable for these batteries. A random sample of23batteries gave a sample variance of14.4months (squared). Using a 0.05 level of significance, test the claim that²= 23 against the claim that²is different from 23.

(a) Find a 90% confidence interval for the population variance. (Round your answers to two decimal places.)

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(b) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

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