The mean time before a certain headache remedy starts to work is 12 minutes with a standard deviation of 3. A new coating is used to help swallow the pill. A sample of 38 people using the pills with the new coating showed the mean time before it started to work was 14 minutes. Is there a difference with the new coating?

Test at the .01 level. State the hypotheses and identify the claim, find the critical value(s), compute the test value, make the decision, and summarize the results.

Solution: We have to test the following hypotheses:

We use a two tailed test z-test (the population variance is known). The critical values for this test are

The rejection region is given by

We compute now the z-statistics:

This means that we reject the null hypothesis. In other words, we have enough evidence to support the claim that there’s a difference with the new coating, at the 0.01 significance level.