EXAMPLE 6.17 Bottle Fill Amount: The Test Statistic

CASE 6.1 For Example 6.13 (page 317), the null hypothesis is , and a sample gave . The test statistic for this problem is the standardized version of :

This statistic is the distance between the sample mean and the hypothesized population mean in the standard scale of -scores. In this example,

Even without a formal probability calculation, by simply recalling the 68–95–99.7 rule for the Normal, we realize that a -score of 3.44 is an unusual value. This suggests incompatibility of the observed sample result with the null hypothesis.