When operating normally, a manufacturing process produces tablets for which the mean weight of the active ingredient is 5 grams, and the standard deviation is .025 gram. For a random sample of twelve tablets, the following weights of active ingredient (in grams) were found: 5.01 4.96 5.00 5.00 5.03 5.03 4.98 4.98 4.95 5.01 5.04 4.95

(a) Without assuming that the population variance is known, test the null hypothesis that the population mean weight of active ingredient per tablet is 5 grams. Use a two-sided alternative and a 5% significance level. State any assumptions that you make.

(b) Stating any assumptions that you make, test the null hypothesis that the population standard deviation is .025 gram against the alternative hypothesis that the population standard deviation exceeds .025 gram. Use a 5% significance level.