A manufacturer produces cement in bags. We randomly pick 16 bags to examine the weights (unit: pounds). Their weights are as follows:

50.6 50.8 49.9 50.3 50.4 51.0 49.7 51.2 51.4 50.5 49.3 49.6 50.6 50.2 50.9 49.6

Suppose the weight of a candy bag is approximately normally distributed.

(a) Find a 95% confidence interval on the mean weight.

(b) Explain the meaning of the confidence interval you found.

(c) The manufacturer claims that the mean weight is 50.4 lbf, but consumer complaints suggest that the manufacturer is underfilling the bags. Conduct the appropriate one-sided hypothesis test using a significance level = 0.05. State the null and alternate hypotheses, identify the rejection and non-rejection regions, compute the test statistic, report the conclusion of the test, and interpret the conclusion.

(d) What is the p-value for the test in part (c)?