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 ?2 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 ?2 = 23 months (squared) is most desirable for these batteries. A random sample of 26 batteries gave a sample variance of 15 months (squared). Using a 0.05 level of significance, test the claim that ?2 = 23 against the claim that ?2 is different from 23.
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 ?2 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 ?2 = 23 months (squared) is most desirable for these batteries. A random sample of 26 batteries gave a sample variance of 15 months (squared). Using a 0.05 level of significance, test the claim that ?2 = 23 against the claim that ?2 is different from 23.
(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)
What are the degrees of freedom?
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