The manufacturer of soap is in the process of producing 48-ounce boxes of detergent. The automated filling device needs frequent checking to verify that it’s actually putting 48 ounces in each box. Box weights are known to be normally distributed with a standard deviation of 0.2 ounces. A sample of 50 boxes is taken and found to have a mean of 47.6 ounces. If you use a .05 significance level, is the machine filling the boxes properly?

Solution: We have the following hypotheses:

We use a Z-test, where the Z-statistic is given by:

We reject the test if, where.That means that we reject the null hypothesis. That means that we accept that the machine is filling the boxes improperly, at the 0.05 significance level.