Chapter 4, Problem 12E

A machine is used to fill containers with a liquid product. Fill volume can be assumed to be normally distributed. A random sample of ten containers is selected, and the net contents (oz) are as follows: 12.03, 12.01, 12.04, 12.02, 12.05, 11.98, 11.96, 12.02, 12.05, and 11.99.

1. (a) Suppose that the manufacturer wants to be sure that the mean net contents exceeds 12 oz. What conclusions can be drawn from the data (use $\alpha =0.01$)?
2. (b) Construct a 95% two-sided confidence interval on the mean fill volume.
3. (c) Does the assumption of normality seem appropriate for the fill volume data?