It is commonly believed that the mean body temperature of a healthy adult is $98.6^{\circ} \mathrm{F}$. You are not entirely convinced. You believe that it is not $98.6^{\circ} \mathrm{F}$. You collected data using 52 healthy people and found that they had a mean body temperature of $98.29^{\circ} \mathrm{F}$ with a standard deviation of $1.02^{\circ} \mathrm{F}$. Use a 0.05 significance level to test the claim that the mean body temperature of a healthy adult is $<$ $98.6^{\circ} \mathrm{F}$. a) Identify the null and alternative hypotheses? \[ \begin{array}{l} H_{0}:(=2) \times \frac{\sigma^{6}}{\square} \\ H_{A_{1}}:(\square) \times \sigma^{\circ} \square \end{array} \] b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)? left-tailed right-tailed two-tailed c) Identify the appropriate significance level. d) Calculate your test statistic. Write the result below, and be sure to round your final answer to 3 decimal places. e) Calculate your p-value. Write the result below, and be sure to round your final answer to 3 decimal places.

Step 1 ：Identify the null and alternative hypotheses. The null hypothesis (H0) is that the mean body temperature of a healthy adult is equal to 98.6 degrees Fahrenheit. The alternative hypothesis (HA) is that the mean body temperature of a healthy adult is less than 98.6 degrees Fahrenheit. So, \(H_{0}: \mu = 98.6^{\circ} \mathrm{F}\), \(H_{A}: \mu < 98.6^{\circ} \mathrm{F}\).

Step 2 ：Determine the type of hypothesis test to conduct. This is a left-tailed test.

Step 3 ：Identify the appropriate significance level. The significance level is 0.05.

Step 4 ：Calculate the test statistic. Given values are sample mean = 98.29, population mean = 98.6, standard deviation = 1.02, and sample size = 52. The test statistic (z) is calculated as \(z = \frac{sample\_mean - population\_mean}{\frac{standard\_deviation}{\sqrt{sample\_size}}}\). The test statistic is approximately -2.192, so \(\boxed{-2.192}\).

Step 5 ：Calculate the p-value. The p-value is calculated using the cumulative distribution function (CDF) of the normal distribution at the calculated z-value. The p-value is approximately 0.014, so \(\boxed{0.014}\).

Step 6 ：Since the p-value is less than the significance level of 0.05, we reject the null hypothesis. There is sufficient evidence to support the claim that the mean body temperature of a healthy adult is less than $98.6^{\circ} \mathrm{F}$.