tions 8-3 \& 8-4 Homework Question 2, 8.3.6-T HW Score: $20 \%, 1$ Points: 0 of 1 Use technology to find the P-value for the hypothesis test described below. The claim is that for $12 \mathrm{AM}$ body temperatures, the mean is $\mu>98.6^{\circ} \mathrm{F}$. The sample size is $n=9$ and the test statistic is $t=1.711$. P-value $=\square_{4}$ (Round to three decimal places as needed. $)$
Solution
Step 1 ：Given that the claim is that for 12 AM body temperatures, the mean is \( \mu > 98.6^{\circ} F \). The sample size is \( n = 9 \) and the test statistic is \( t = 1.711 \).
Step 2 ：We need to find the P-value for this hypothesis test.
Step 3 ：The P-value is calculated using the t-distribution with \( t = 1.711 \) and degrees of freedom \( df = n - 1 = 9 - 1 = 8 \).
Step 4 ：The P-value is the probability of observing a test statistic as extreme as 1.711 or more, under the null hypothesis.
Step 5 ：Using the t-distribution, the P-value is calculated to be approximately 0.0627.
Step 6 ：This P-value is used to make a decision in the hypothesis test. If the P-value is less than the significance level (usually 0.05), we reject the null hypothesis.
Step 7 ：In this case, the P-value is greater than 0.05, so we would not reject the null hypothesis that the mean body temperature at 12 AM is 98.6 degrees Fahrenheit.
Step 8 ：Final Answer: The P-value is approximately \(\boxed{0.063}\).
