Question: A machine produces 3-inch nails. A sample of 12 nails was selected and their lengths determined. The results are as follows:
2.94 2.96 3.01 3.01 3.03 3.03 3.03 3.03 3.07 2.93 3.00 3.07
Assuming that a = 0.01, 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?