A process that produces bottles of shampoo, when operating correctly, produces bottles whose contents weight, on average, 20 ounces. A random sample of nine bottles from a single production run yields the following content weights in ounces

21.4 19.7 19.7 20.6 20.820.1 19.7 20.3 20.9

Assuming that the population distribution is normal:

(a) Test at the 5% level against a two-sided alternative the null hypothesis that the process is operating correctly. (Again, use the P-value method.)

(b) Test at a 10% level of significance that the mean is greater than 20 ounces. (Use the P-value method.)