To answer this, let's denote the known parameters:

1. Let $\mu_0$ represent the commonly believed mean body temperature of a healthy adult.
2. Let $\bar{x}$ represent the mean body temperature from your sample of 39 healthy individuals.
3. Let $s$ be the standard deviation of the sample.
4. The significance level is $\alpha = 0.05$.

Part (d): Calculate the Test Statistic

For a hypothesis test regarding the mean when the population standard deviation is unknown, we use a t-test. The test statistic $t$ is calculated as follows:

$t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}$

where:

• $\bar{x}$ = sample mean body temperature
• $\mu_0$ = hypothesized mean body temperature
• $s$ = sample standard deviation
• $n$ = sample size (39 in this case)

Part (e): Calculate the p-value

Since this is a two-tailed test, we need to find the probability that the test statistic is at least as extreme as the observed value (in both directions). This requires calculating the p-value based on the t-distribution with $n - 1$ (i.e., 38) degrees of freedom.

If you provide the actual values for $\mu_0$, $\bar{x}$, and $s$, I can complete the calculations for you.