It has long been stated that the mean temperature of humans is $98.6^{\circ} \mathrm{F}$. However, two researchers currently involved in the subject thought that the mean temperature of humans is less than $98.6^{\circ} \mathrm{F}$. They measured the temperatures of 111 healthy adults 1 to 4 times daily for 3 days, obtaining 500 measurements. The sample data resulted in a sample mean of $98.5^{\circ} \mathrm{F}$ and a sample standard deviation of $0.8^{\circ} \mathrm{F}$. Use the P-value approach to conduct a hypothesis test to judge whether the mean temperature of humans is less than $98.6^{\circ} \mathrm{F}$ at the $\alpha=0.01$ level of significance

Step 1 ：State the null hypothesis \( H_0: \mu = 98.6^{\circ} \mathrm{F} \) and the alternative hypothesis \( H_a: \mu < 98.6^{\circ} \mathrm{F} \)

Step 2 ：Calculate the test statistic using the formula \( t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \) where \( \bar{x} \) is the sample mean, \( \mu \) is the hypothesized mean, \( s \) is the sample standard deviation, and \( n \) is the sample size

Step 3 ：Find the P-value associated with the calculated test statistic

Step 4 ：Compare the P-value to the significance level \( \alpha = 0.01 \)

Step 5 ：If the P-value is less than \( \alpha \), reject the null hypothesis

Step 6 ：Since the P-value \( 0.0027 \) is less than the significance level \( \alpha = 0.01 \), we reject the null hypothesis

Step 7 ：Conclude that the mean temperature of humans is less than \( 98.6^{\circ} \mathrm{F} \)

Step 8 ：The final answer is \( \boxed{\text{Reject } H_0} \)