Question

A professional tennis player has a serve-return rate of p = 0.71. A random sample of 55 serve returns is selected. Which of the following is the mean of the sampling distribution of p hat ?

Mu Subscript p hat Baseline = p = 0.71
Mu Subscript p hat Baseline = n p = 55 (0.71) = 39.05
Mu Subscript p hat Baseline = 1 minus p = 1 minus 0.71 = 0.29
Mu Subscript p hat Baseline = n (1 minus p) = 55 (1 minus 0.71) = 15.95

Answer 1

The mean of the sampling distribution of p hat is the proportion itself, which is p. In this case, Mu Subscript p hat Baseline equals p equals 0.71, not multiplied by the sample size or any other variation.

Step-by-step explanation:

The correct mean of the sampling distribution of π hat (μ_π hat) for a proportion is simply the proportion itself, which is π (p). Therefore, if a professional tennis player has a serve-return rate of p = 0.71, the mean of the sampling distribution of p hat would be:

μ_π hat = p = 0.71

This is because we're looking at the proportion of successful serve returns in a sample of attempts. The size of the sample (n) does not affect the mean of the sampling distribution of the proportion.

The idea here is based on the properties of the binomial distribution, as each serve return can be considered as a Bernoulli trial where there are only two possible outcomes: a success (returning the serve) or a failure (not returning the serve).

Answer 2

I would say A is the answer