Food Manufacturing Statistics

As part of its quality control system, a major food manufacturer sampled ten 8 ounce boxes of cereal. The objective of the sample was to decide whether the box filling process was ensuring that every box contained at least 8 ounces of cereal. Each sample was weighed with the following results (in ounces): 8.10, 8.20, 8.05, 8.15, 8.25, 8.15, 8.05, 8.25, 8.20 and 8.00.

The mean sample weight was 8.14 ounces with a standard deviation of 0.09.

a). Based on this sample can the manufacturer be 95% confident that the typical (average of all boxes) of cereal produced is at least 8 ounces? Test using a two-sided hypothesis test. Be sure to show your null and alternative hypothesis and your calculations.

b). Calculate the P-value using the T distribution rather the Z distribution as sample size is small.

c). Can the manufacturer be confident that the filling process results in 95% of all boxes containing at least 8 ounces? (this is not asking about whether the average is different than 8, but rather whether more than 19 out of 20 boxes will have at least 8 ounces).