3. A tile company advertises that it will deliver your tile within 15 days of your purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 with a standard deviation of 5.6 days. Using a p-value, test the hypothesis at the 5% level of significance.

Solution: We want to the two-tailed hypotheses

wherecorresponds to the mean delivery time. In order to test the hypotheses, we define the following statistic:

and corresponds to the standard deviation, corresponds to the sample size. We reject the null hypothesis if , where corresponds as usual to the cutoff point to the standard normal distribution. Since we want 95% confidence level, we take, and as before get that. We calculate to get

For this we get a p-value of, so the p-value is not significant, because it’s not less that 0.05. Therefore, we don’t have enough evidence to reject the null hypothesis. Notice that if we test the one-tailed hypothesis

we would get a p-value of 0.0668, which is still not significant, therefore, we couldn’t reject the null hypothesis either.