mathschallenge.net

Problem

The contents of twelve boxes of matches were recorded as:

34, 31, 29, 35, 33, 30, 31, 28, 27, 35, 32, 31

On the box it stated, "Average contents 32 matches", but the sample mean can be shown to be about 31.3.

When the company received a complaint that the average contents is less than 32, they claimed that approximately one in five samples of size twelve would have a mean less than 31.3.

By using the sample data, test this claim and determine the minimum sample mean before the claim can be rejected at a 5% significance level.