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 s² 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 all at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of s² = 23 months (squared) is most desirable for these batteries. A random sample of 22 batteries gave a sample variance of 14.3 months (squared).

(i) Using a 0.05 level of signifi­cance, test the claim that s² = 23 against the claim that s² is different from 23.

(ii) Find a 90% confi­dence interval for the population variance s².

(iii) Find a 90% con­fidence interval for the population standard deviation s.