A scientist claims that a smaller proportion of members of the National Academy of Sciences are women when compared to the proportion of women nationwide. Let p1 represent the proportion of women in the National Academy of Sciences and p2 represent the proportion of women nationwide. Which is the correct alternative hypotheses that corresponds to this claim?

A. Ha: p1 - p2 < 0

B. Ha: p1 - p2 > 0

C. Ha: p1 - p2? 0

Correct option: (A) p₁ - p₂ < 0.

Step-by-step explanation:

The claim made by the scientist is that the proportion of female members of the National Academy of Sciences is less than the proportion of female members nationwide.

To test this claim we can difference between two proportions z-test.

It is assumed that p₁ is the proportion of women in the National Academy of Sciences and p₂ is the proportion of women nationwide.

Then we nee to test whether p₁ - p₂ < 0 or not.

The hypothesis can be defined as:

H₀: The proportion of women in the National Academy of Sciences is not less than the proportion nationwide, i. e. p₁ - p₂ ≥ 0.

H₀: The proportion of women in the National Academy of Sciences is less than the proportion nationwide, i. e. p₁ - p₂ < 0.

Thus, the correct option is (A).