What are the null and alternative hypotheses described for the comparison?

What are the null and alternative hypotheses described for the comparison?

• A. Ho: p_depression > p_none; Ha: p_depression ≤ p_none
• B. Ho: p_depression ≠ p_none; Ha: p_depression = p_none
• C. Ho: p_depression = p_none; Ha: p_depression > p_none
• D. Ho: p_depression = p_none; Ha: p_depression ≠ p_none

Answer: (D)

When you’re comparing two proportions, you test whether there is any difference between them. The null hypothesis assumes no difference, meaning the two proportions are equal. The alternative claims there is a difference, meaning the two proportions are not equal. This is a two-sided test because we’re checking for any difference in either direction, not a specific increase or decrease in one group. So the correct description is: the null is that the two proportions are equal, and the alternative is that they are not equal. This captures testing for a difference without assuming which group is higher. The other option formats would imply a one-sided test or misstate the relationship, which is not what’s being asked.

When you’re comparing two proportions, you test whether there is any difference between them. The null hypothesis assumes no difference, meaning the two proportions are equal. The alternative claims there is a difference, meaning the two proportions are not equal. This is a two-sided test because we’re checking for any difference in either direction, not a specific increase or decrease in one group.

So the correct description is: the null is that the two proportions are equal, and the alternative is that they are not equal. This captures testing for a difference without assuming which group is higher. The other option formats would imply a one-sided test or misstate the relationship, which is not what’s being asked.