Let's analyze the situation to answer the questions.

(b) Type of Error When Not Rejecting the Null Hypothesis:

• Null Hypothesis ($H_0$): The mean systolic blood pressure $\mu$ of CEOs is 136 mm Hg.
• Alternative Hypothesis ($H_1$): The mean systolic blood pressure $\mu$ of CEOs is more than 136 mm Hg.

If the researcher decides not to reject the null hypothesis, the type of error he might be making is a Type II error.

• Type II error occurs when the researcher fails to reject a false null hypothesis. In this context, it means that the true mean systolic blood pressure is actually greater than 136 mm Hg, but the researcher incorrectly concludes that it is not.

(c) Describing a Type I Error:

A Type I error occurs when the researcher rejects a true null hypothesis. Let's fill in the blanks to describe this scenario:

• Null Hypothesis ($H_0$): The mean systolic blood pressure $\mu$ of CEOs is 136 mm Hg.
• Alternative Hypothesis ($H_1$): The mean systolic blood pressure $\mu$ of CEOs is more than 136 mm Hg.

If the true mean systolic blood pressure of CEOs of major corporations is 136 mm Hg, then a Type I error would be rejecting the hypothesis that $\mu = 136$ mm Hg.

Summary:

• (b) Type of error if not rejecting $H_0$: Type II error.
• (c) Type I error description: A Type I error would be rejecting the hypothesis that $\mu = 136$ mm Hg when it is actually true.

Would you like further details or explanations on any of these concepts?

Related Questions:

1. What is the significance level ($\alpha$) in hypothesis testing, and how does it relate to Type I error?
2. What is the power of a statistical test, and how is it related to Type II error?
3. How do sample size and standard deviation affect the likelihood of making a Type II error?
4. What are the consequences of a Type I error in a medical context?
5. Can you explain the relationship between confidence intervals and hypothesis testing?
6. How would you calculate the test statistic for the given sample data?
7. What are the assumptions required for conducting a hypothesis test on the mean?
8. How does the choice of one-tailed vs. two-tailed tests affect the outcomes of hypothesis testing?

Tip: Always clearly define your null and alternative hypotheses before conducting a statistical test to avoid confusion and errors in interpretation.