Let's analyze this question regarding null and alternative hypotheses.

Problem Analysis

The problem states:

• The proportion of U.S. adults aged 25 or older who smoke is 0.22.
• A researcher suspects that this rate is lower among U.S. adults with a bachelor's degree or higher.

This setup indicates a one-sided hypothesis test where the researcher is testing if the proportion is less than 0.22 for the group with higher education.

Null and Alternative Hypotheses

1. Null Hypothesis (H₀): The null hypothesis typically states that there is no effect or no difference from the standard. In this case, it means that the proportion of smokers among U.S. adults aged 25 or older with a bachelor's degree or higher is equal to the general population proportion of 0.22.

   • Correct Answer: "The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is 0.22."

2. Alternative Hypothesis (Hₐ): The alternative hypothesis aligns with the researcher's suspicion that the rate is lower than 0.22 for those with higher education.

   • Correct Answer: "The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is less than 0.22."

Final Answers

• Null Hypothesis: "The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is 0.22."
• Alternative Hypothesis: "The proportion of smokers among U.S. adults 25 or older who have a bachelor's degree or higher is less than 0.22."

Would you like further details on hypothesis testing concepts, or do you have any questions?

Here are five questions that expand on this content:

1. What are the possible types of errors in hypothesis testing?
2. How would you calculate the test statistic for this hypothesis test?
3. What is the significance level, and how does it affect hypothesis testing?
4. Why is this a one-sided test instead of a two-sided test?
5. How does sample size impact the outcome of hypothesis testing?

Tip: When formulating hypotheses, the null hypothesis (H₀) usually reflects the "status quo" or no change, while the alternative hypothesis (Hₐ) represents the research question or the effect being tested.