Chapter 10.3, Problem 30AYU

Problem 26

24. Filling Bottles A certain brand of apple juice is supposed to have 64 ounces of juice. Because the penalty for underfilling bottles is severe, the target mean amount of juice is 64.05 ounces. However, the filling machine is not precise, and the exact amount of juice varies from bottle to bottle. The quality-control manager wishes to verify that the mean amount of juice in each bottle is 64.05 ounces so that she can be sure that the machine is not over- or underfilling. She randomly samples 22 bottles of juice, measures the content, and obtains the following data:

A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot does not show any outliers.

1. a. Should the assembly line be shut down so that the machine can be recalibrated? Use a 0.01 level of significance.
2. b. Explain why a level of significance of α = 0.01 is more reasonable than α = 0.1. [Hint: Consider the consequences of incorrectly rejecting the null hypothesis.]