To solve for parts $c$ and $d$, let's go through the necessary steps for a one-sample t-test for the mean.

Given Data:

Temperatures (sample): $99.7, 98.4, 100.1, 98, 100.9, 96.9, 98.3, 97.1, 99.3, 100.3, 100.4, 98.6, 97.5, 98.5, 96.9, 98.1$ Sample size ($n$) = 16
Population mean ($\mu_0$) = 98.6
Significance level ($\alpha$) = 0.10

Steps to solve:

1. Calculate the Sample Mean ($\bar{x}$): Sum all the given temperatures and divide by the sample size.

2. Calculate the Sample Standard Deviation ($s$): Use the formula for standard deviation to find $s$ from the sample data.

3. Compute the Test Statistic: The formula for the t-statistic in a one-sample t-test is: $t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}$

4. Determine the p-value: For a one-tailed test, calculate the p-value based on the calculated t-statistic and the degrees of freedom ($df = n - 1$).

I’ll calculate the exact values for steps $c$ and $d$.The calculations yield the following results:

• c. The test statistic $t$ = 0.270 (rounded to three decimal places).
• d. The p-value = 0.3955 (rounded to four decimal places).

Would you like further clarification on these results or help with the next steps?

Here are five related questions to expand your understanding:

1. How is the t-statistic calculated for a one-sample t-test?
2. What does a high p-value indicate about the null hypothesis?
3. Why is it important to round values in hypothesis testing?
4. How does the significance level ($\alpha$) influence the conclusion of the test?
5. What are degrees of freedom, and why do they matter in t-tests?

Tip: In hypothesis testing, a p-value higher than the significance level suggests that the data does not provide strong evidence against the null hypothesis.