Recall the quality-control study in Example 7.5, in which we tested to determine whether a cereal box filling machine was deviating from the specified mean fill of μ = 12 ounces. The test setup is repeated here:

Note that two rejection regions have been specified corresponding to values of α = .05 and α = .01, respectively. Assume that n = 100 and s = .5.

a. Suppose the machine is underfilling the boxes by an average of .1 ounce (i.e., μ = 11.9). Calculate the values of β corresponding to the two rejection regions.

Discuss the relationship between the values of α and β.

b. Calculate the power of the test for each of the rejection regions when μ = 11.9.

Examples 7.5

Refer to the quality-control test set up in Example 7.3. Recall that a machine is designed to discharge a mean of 12 ounces of cereal per box. A sample of 100 boxes yielded the fill amounts (in ounces) shown in Table 7.3. Use these data to conduct the following test:

Example 7.3

A manufacturer of cereal wants to test the performance of one of its filling machines.

The machine is designed to discharge a mean amount of 12 ounces per box, and the manufacturer wants to detect any departure from this setting. This quality study calls for randomly sampling 100 boxes from today’s production run and determining whether the mean fill for the run is 12 ounces per box. Set up a test of hypothesis for this study, using α = .01.

Transcribed Image Text:

Ho: μ = 12 H: μ # 12 (i.e., μ < 12 or p > 12) x 12 OT Rejection region: z < -1.96 or z> 1.96 for α = .05 Z < -2.575 or z> 2.575 for a = .01 Test statistic: z =