Step 1 :First, we need to determine the null and alternative hypotheses. The null hypothesis \(H_{0}\) is that the population mean is 98.6 degrees Fahrenheit, and the alternative hypothesis \(H_{a}\) is that the population mean is not 98.6 degrees Fahrenheit. So, we have \(H_{0}: \mu=98.6\) and \(H_{a}: \mu \neq 98.6\).
Step 2 :Next, we check the conditions to see whether the test statistic will follow a t-distribution. The sample is random and the observations are independent. The distribution of the sample is approximately Normal.
Step 3 :Then, we find the test statistic. The test statistic is \(t=-1.12\).
Step 4 :Finally, we find the p-value. The p-value is the probability of obtaining a test statistic as extreme as -1.12, or more extreme, under the assumption that the null hypothesis is true. Using the formula for the p-value with a t-distribution, we find that the p-value is approximately 0.292.
Step 5 :The final answer is that the p-value is approximately \(\boxed{0.292}\).