(deciding whether to use the pooled sample variance). Each day properly inflated basketballs lose pressure. A manufacturer is trying to identify if a new interior lining will prolong the useable inflation life of a certain type of its basketballs. The study determined the number of days it takes for a properly inflated basketball to lose 5% of its pressure. It was found that in a sample of 10 regular basketballs the mean useable life was 28.5 days, with a standard deviation of 3.5 days, while in a sample of 10 specially-lined basketballs the mean useable life was 31.2 days with a standard deviation of 2.2 days (these are all sample means and standard deviations). Assume that the useable lifetimes for both regular and new-lining basketballs follow a Normal distribution. (a) Test if the variances are the same in these populations, at the a = 0.05 significance level. (b) Develop a two-sided statistical hypothesis test to determine if there is a difference in mean and usable lifetime at the a = 0.05 significance level. Be sure to state the null and alternative hypotheses, the test statistic, state a rejection region (i.e. find the appropriate critical values) or compute a p-value, and draw a conclusion. Depending on the outcome of the test in part (a), determine whether or not you should use the pooled sample variance for the computation of the standard error in part (b).