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 0.025 gram. For a random sample of 12 tablets the

following weights of active ingredient (in grams) were

found:

5.01 4.69 5.03 4.98 4.98 4.95

5.00 5.00 5.03 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 0.025 gram against the alternative

hypothesis that the population standard deviation

exceeds 0.025 gram. Use a 5% significance level.