Step 1: Formulating the Hypotheses

Given that we're testing whether the mean body temperature is different from 98.60°F, we need to formulate the null and alternative hypotheses:

• Null Hypothesis (H₀): The mean body temperature of healthy adults is 98.60°F.
  $H_0: \mu = 98.60$

• Alternative Hypothesis (H₁): The mean body temperature of healthy adults is not 98.60°F (two-tailed test).
  $H_1: \mu \neq 98.60$

Step 2: Test Statistic Calculation

To test the hypothesis, we use the z-test formula because the population standard deviation ($\sigma$) is known:

$z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}}$

Where:

• $\bar{x} = 98.20$ is the sample mean.
• $\mu_0 = 98.60$ is the population mean under the null hypothesis.
• $\sigma = 0.62$ is the population standard deviation.
• $n = 106$ is the sample size.

Now, substitute the values into the formula:

$z = \frac{98.20 - 98.60}{\frac{0.62}{\sqrt{106}}}$

Let's calculate the test statistic:

$z = \frac{-0.40}{\frac{0.62}{\sqrt{106}}} = \frac{-0.40}{0.0601} \approx -6.66$

Step 3: Finding the P-value

The z-value we found is approximately $-6.66$. For a two-tailed test, the p-value corresponds to the area under the standard normal curve that is more extreme than the absolute value of the test statistic (since the alternative hypothesis is $\mu \neq 98.60$).

Using the z-table or a statistical tool to find the p-value corresponding to $z = -6.66$, we find that the p-value is extremely small, essentially 0.

Step 4: Decision Rule

At a significance level of $\alpha = 0.05$, if the p-value is less than 0.05, we reject the null hypothesis.

Since the p-value is 0.00, which is less than 0.05, we reject the null hypothesis.

Conclusion

Question 4 (Test p-value):
The p-value is 0.00. Therefore, the correct answer is 0.00.

Question 5 (State the Conclusion):
Since the p-value is smaller than the significance level, we reject the null hypothesis. Therefore, the correct conclusion is:
Reject H₀.

Summary of Answers:

• Question 4: 0.00
• Question 5: Reject H₀

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Would you like more details on the test calculation or any clarifications?

Here are a few related questions you might find interesting:

1. How do you calculate a confidence interval for the population mean when the population standard deviation is known?
2. What is the difference between a one-tailed and a two-tailed hypothesis test?
3. How do you interpret a p-value of 0.03 in hypothesis testing?
4. Why is it important to know whether the population standard deviation is known or not in hypothesis testing?
5. What are the assumptions underlying the z-test for a population mean?

Tip: When performing hypothesis tests, always double-check if the test statistic corresponds to the correct distribution (z-test for known $\sigma$, t-test for unknown $\sigma$, etc.).