Answer:
Correct option: (A) <em>p</em>₁ - <em>p</em>₂ < 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 <em>z</em>-test.
It is assumed that <em>p</em>₁ is the proportion of women in the National Academy of Sciences and <em>p</em>₂ is the proportion of women nationwide.
Then we nee to test whether <em>p</em>₁ - <em>p</em>₂ < 0 or not.
The hypothesis can be defined as:
<em>H₀</em>: The proportion of women in the National Academy of Sciences is not less than the proportion nationwide, i.e. <em>p</em>₁ - <em>p</em>₂ ≥ 0.
<em>H₀</em>: The proportion of women in the National Academy of Sciences is less than the proportion nationwide, i.e. <em>p</em>₁ - <em>p</em>₂ < 0.
Thus, the correct option is (A).