To address the question in the image, the problem involves determining the null hypothesis ($H_0$) and the alternative hypothesis ($H_1$) for a claim about a proportion ($p$).

The researcher claims that 62% of voters favor gun control. This involves a population proportion ($p$), so we need to set up hypotheses about this proportion.

Hypotheses:

1. Null Hypothesis ($H_0$): This represents the status quo or no change from the claim.
   $H_0: p = 0.62$ This states that the proportion of voters who favor gun control is 62%.

2. Alternative Hypothesis ($H_1$): This is what the researcher is testing against $H_0$. Depending on the context (e.g., whether this is a two-tailed, left-tailed, or right-tailed test), $H_1$ could take different forms:

   • If the researcher wants to check if the proportion is not equal to 62%, the alternative hypothesis is: $H_1: p \neq 0.62$
   • If the researcher wants to check if the proportion is less than 62%, the alternative hypothesis is: $H_1: p < 0.62$
   • If the researcher wants to check if the proportion is greater than 62%, the alternative hypothesis is: $H_1: p > 0.62$

The exact form of $H_1$ depends on the context of the test (e.g., what the researcher is investigating or suspecting).

Would you like further clarification or help with setting up the test context?

Follow-up Questions:

1. What type of test (two-tailed, left-tailed, or right-tailed) would be most appropriate here?
2. How is the significance level ($\alpha$) determined for this hypothesis test?
3. What steps are involved in testing this hypothesis with sample data?
4. How would sample size affect the test's reliability and accuracy?
5. Can you interpret a p-value in the context of this problem?

Tip:

When forming hypotheses, always carefully read the claim to decide if it should be included in the null or alternative hypothesis.