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 still 500 so i am confused even though we know 250 men and 250 women.

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Expert Solution

Answer :

Here the difference between both (a) and (b) is sample size may be same for both questions but the male(70%) and female (30%) varies here both male and female samples given n₁ = 250 and n₂ = 250

so considering the samples separately 250 for men and another 250 for women so we are not adding here taking separately as n₁ = 250 and n₂ = 250

orchestra answered 1 year ago

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