4
QuizMultiple Choice

Sampling Distribution of the Sample Proportion — Quiz

Question 4 • Math 4

The proportion of twins born in a town is p is equal to 0 point 1 2 Suppose we randomly select 100 women from this town who give birth in the next year. Which of the following is the mean of the sampling distribution of hat p ?

Answer
A
mu sub hat p is equal to n p is equal to 100 times 0 point 1 2 is equal to 12
B
mu sub hat p is equal to p is equal to 0 point 1 2
C
mu sub hat p is equal to 1 minus p is equal to 1 minus 0 point 1 2 is equal to 0 point 8 8
D
mu sub hat p is equal to n times open paren 1 minus p close paren is equal to 100 times open paren 1 minus 0 point 1 2 close paren is equal to 88

Explanation

The mean of the sampling distribution of a sample proportion, p̂, equals the population proportion p. Here, p = 0.12, so the mean is 0.12, regardless of the sample size of 100. Therefore, choice B, “μ of p̂ equals p equals 0.12,” is correct.

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