Question
Suppose that 70% of men and 30% of women in a state support the incumbent candidate...
Suppose that 70% of men and 30% of women in a state support the incumbent candidate for the governor. Assume that the numbers of men and women in the state are equal.
(a) Suppose 500 people are surveyed at random, and ^p1 is the proportion of people surveyed who say they support the incumbent. What is the variance of ^p1?
(b) Suppose that 250 men and 250 women are surveyed at random, and ^p2 is the proportion of people surveyed who say they support the incumbent. What is the variance of ^p2?
(c) Calculate the relative efficiency of ^p2 with respect to ^p1
Before you answer the question, please tell me that what the difference is between question (a) and (b) because the sample size is same 500 and i have no idea why in part(b) we need to use 250 for our sample size for woman and 250 sample size for men.
Please explain the logics behind it why it will make the variance different
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