Suppose a simple random sample of 1200 adults is selected from a large population in which the proportion of adults who support a certain policy is $p$. What is the mean of the sampling distribution of the sample proportion $\bar{p}$?

• A. $\sqrt{\frac{p(1-p)}{1200}}$
• B. $0.5$
• C. $\frac{1}{1200}$
• D. $p$

Answer: (D)

Verified step by step guidance

1. Identify the parameter of interest: the population proportion \( p \) represents the true proportion of adults who support the policy in the entire population.
2. Recognize that the sample proportion \( \hat{p} \) is a random variable representing the proportion of adults who support the policy in the sample of size 1200.
3. Recall that the sampling distribution of the sample proportion \( \hat{p} \) has a mean equal to the population proportion \( p \). This is because \( \hat{p} \) is an unbiased estimator of \( p \).
4. Express the mean of the sampling distribution of \( \hat{p} \) as \( E(\hat{p}) = p \).
5. Note that the other options given (such as the standard error formula \( \sqrt{\frac{p(1-p)}{1200}} \), 0.5, or \( \frac{1}{1200} \)) do not represent the mean of the sampling distribution but rather relate to variability or specific values.