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Multiple choice: Select the best answer for Exercises 43 to 46 . Exercises 43 to 45 refer to the following setting. The magazine Sports Illustrated asked a random sample of 750 Division I college athletes, "Do you believe performanceenhancing drugs are a problem in college sports?" Suppose that
30% of all Division I athletes think that these drugs are a problem. Let
hat(p) be the sample proportion who say that these drugs are a problem.
43. Which of the following are the mean and standard deviation of the sampling distribution of the sample proportion
hat(p) ?

Multiple choice: Select the best answer for Exercises $43$ to $46$ . Exercises $43$ to $45$ refer to the following setting. The magazine Sports Illustrated asked a random sample of $750$ Division I college athletes,

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Find values of normal variables

Full solution

Q. Multiple choice: Select the best answer for Exercises

43

to

46

. Exercises

43

to

45

refer to the following setting. The magazine Sports Illustrated asked a random sample of

750

Division I college athletes,

Calculate mean: Calculate the mean of the sampling distribution of the sample proportion $\hat{p}$ . The mean of the sampling distribution of the sample proportion is equal to the population proportion, which is given as $30\%$ or $0.30$ .
Calculate standard deviation: Calculate the standard deviation of the sampling distribution of the sample proportion $\hat{p}$ . The standard deviation of the sampling distribution of the sample proportion is calculated using the formula: $\sigma_{\hat{p}} = \sqrt{\frac{p(1 - p)}{n}}$ where $p$ is the population proportion and $n$ is the sample size.
Perform calculation: Perform the calculation using the values provided. $\newline$ $p = 0.30$ (population proportion) $\newline$ $n = 750$ (sample size) $\newline$ $\sigma_{\hat{p}} = \sqrt{0.30 \times (1 - 0.30) / 750}$ $\newline$ $\sigma_{\hat{p}} = \sqrt{0.30 \times 0.70 / 750}$ $\newline$ $\sigma_{\hat{p}} = \sqrt{0.21 / 750}$ $\newline$ $\sigma_{\hat{p}} = \sqrt{0.00028}$ $\newline$ $\sigma_{\hat{p}} = 0.0167$

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