urrent Attempt in Progress Use the t-distribution and the sample results to complete the test of the hypotheses. Use a $5 \%$ significance level. Assume the resi come from a random sample, and if the sample size is small, assume the underlying distribution is relatively normal. Test $H_{0}: \mu=15$ vs $H_{a}: \mu>15$ using the sample results $\bar{x}=17.2, s=6.4$, with $n=40$. Part 1 (a) Give the test statistic and the $p$-value. Round your answer for the test statistic to two decimal places and your answer for the $p$-value to three decimal places. test statistic $=\mathbf{i}$ $p$-value $=i$

Step 1 ：The problem is asking to perform a one-tailed t-test to test the hypothesis that the population mean is greater than 15. The sample mean is given as 17.2, the sample standard deviation is 6.4, and the sample size is 40.

Step 2 ：The test statistic for a t-test is calculated as (sample mean - population mean) / (sample standard deviation / sqrt(sample size)).

Step 3 ：Using the given values, the test statistic is calculated as \((17.2 - 15) / (6.4 / \sqrt{40})\), which equals 2.17406589136576.

Step 4 ：The p-value can be found by looking up the test statistic in a t-distribution table. The p-value corresponding to the test statistic 2.17406589136576 is 0.017915923344657858.

Step 5 ：Rounding the test statistic to two decimal places and the p-value to three decimal places, we get the test statistic as 2.17 and the p-value as 0.018.

Step 6 ：Final Answer: The test statistic is \(\boxed{2.17}\) and the p-value is \(\boxed{0.018}\).