Question: A machine produces 3-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:

3.02 2.95 2.96 2.96 2.90 2.92 3.02 2.93 3.07 3.07 3.00 2.91
Assuming that = 0.05, test the hypothesis that the population mean is equal to 3.

? State the null and alternate hypotheses

? Calculate the mean and standard deviation

? Determine which test statistic applies, and calculate it

? Determine the critical value(s).

? State your decision: Should the null hypothesis be rejected?