Question

question 12 (1 point)

solve the problem.

a random sample of \\(n = 100\\) measurements is drawn from a binomial population with probability of success .21. give the mean and the standard deviation of the sampling distribution of the sample proportion, \\(\hat{p}\\).

( ) .21; .02
( ) .21; .407
( ) .21; .041
( ) .21; .008

Explanation:

Identify the given parameters

Using the Sampling Distribution of the Sample Proportion knowledge point

$$
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Calculate the mean of the sampling distribution

Using the Sampling Distribution of the Sample Proportion knowledge point

$$ \mu_{\hat{p}} = p = 0.21 $$

Calculate the standard error of the proportion

Using the Standard Error of the Proportion knowledge point

$$ \sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.21 \times 0.79}{100}} = \sqrt{\frac{0.1659}{100}} = \sqrt{0.001659} \approx 0.04073 $$

Match the calculated values with the options

Using the Standard Error of the Proportion knowledge point

$$
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$$

Answer:

• .21; .02
• .21; .407
• .21; .041 (Correct answer)
• .21; .008