8
QuizMultiple Choice

Sampling Distribution of the Sample Proportion — Quiz

Question 8 • Math 4

A professional tennis player has a serve-return rate of p is equal to 0 point 7 1 A random sample of 55 serve returns is selected. Which of the following is the mean of the sampling distribution of hat p ?

Answer
A
mu sub hat p is equal to n times open paren 1 minus p close paren is equal to 55 times open paren 1 minus 0 point 7 1 close paren is equal to 15 point 9 5
B
mu sub hat p is equal to n p is equal to 55 times 0 point 7 1 is equal to 39 point 0 5
C
mu sub hat p is equal to p is equal to 0 point 7 1
D
mu sub hat p is equal to 1 minus p is equal to 1 minus 0 point 7 1 is equal to 0 point 2 9

Explanation

The mean of the sampling distribution of the sample proportion, p-hat, is the population proportion p. Here, p = 0.71, so the mean is 0.71. The sample size affects the variability of p-hat, but not its mean; therefore the correct choice is “mu sub hat p is equal to p is equal to 0.71.”

AI-written and checked against the verified answer.

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