Question: 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.