[EX09-184] The foreman in Exercise 9.183 believes that the cereal-filling machine used for Corn Flakes needs to be replaced and that the new one he is considering will pay for the upgrade within a short time, mainly due to less variability in the fill amount. The new machine is started, and a test run is made. Twenty of these boxes were randomly selected from the run and the contents weighed (in ounces). 14.17 14.25 14.17 14.16 14.18 14.09 14.19 14.17 14.16 14.06 14.11 14.15 14.12 14.19 14.14 14.19 14.13 14.12 14.16 14.15

a. Draw a histogram of the weight of cereal per box.

b. Find the sample statistics mean and standard deviation.

c. What percent of the sample from the new machine is below the 14.0 oz weight?

The foreman needs to estimate the mean weight and test the standard deviation of all boxes being filled.

d. Determine whether an assumption of normality is reasonable. Explain.

e. Find the 95% confidence interval for the mean weight.

f. The filling process for the new machine is claimed to be running with a standard deviation of fill of less than 0.1 oz. Test this hypothesis at the 0.01 level.