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 61 healthy adults 1 to 4 times daily for 3 days, obtaining 275 measurements. The sample data resulted in a sample mean of $98.4^{\circ} \mathrm{F}$ and a sample standard deviation of $1^{\circ} \mathrm{F}$. Use the $\mathrm{P}$-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.

Find the test statistic.
\[
t_{0}=\square
\]
(Round to two decimal places as needed.)
The P-value is $\square$.
(Round to three decimal places as needed.)

Step 1 ：Given in the problem, we have: \(\bar{X} = 98.4\degree F\), \(\mu = 98.6\degree F\), \(s = 1\degree F\), and \(n = 275\).

Step 2 ：We will use the formula for the t-test statistic, which is: \(t = \frac{\bar{X} - \mu}{s / \sqrt{n}}\).

Step 3 ：Substituting these values into the formula, we get: \(t = \frac{98.4 - 98.6}{1 / \sqrt{275}} = -0.2 / (1 / \sqrt{275})\).

Step 4 ：Calculating the denominator first: \(1 / \sqrt{275} \approx 0.0603\).

Step 5 ：Then substitute this into the equation: \(t = -0.2 / 0.0603 \approx -3.32\).

Step 6 ：So, the test statistic \(t_0\) is approximately \(-3.32\) (rounded to two decimal places).

Step 7 ：Next, we need to find the P-value. The P-value is the probability of obtaining a result as extreme as the observed data, assuming that the null hypothesis is true.

Step 8 ：Since we are conducting a one-tailed test (we are testing whether the mean temperature is less than \(98.6\degree F\)), we will look up the P-value corresponding to our t statistic in a t-distribution table or use a statistical software or calculator.

Step 9 ：Unfortunately, without a t-distribution table or software, we cannot calculate the exact P-value here. However, given that our t statistic is \(-3.32\) and we have a large sample size (275), we can say that our P-value will be very small and likely less than our significance level of 0.01.

Step 10 ：Therefore, we would reject the null hypothesis and conclude that the mean temperature of humans is less than \(98.6\degree F\).

Step 11 ：The final answer is \(\boxed{-3.32}\).