Question

The United States government wanted to determine what proportion of Americans approve of the current President so they conducted a survey of 2,000 randomly chosen Americans. Assume that the true proportion of Americans who approve of the president is 0.46. Determine what the mean and the standard deviation of the sampling distribution of the sample proportion would be. Round to 2 decimal places when necessary. The mean of the sampling distribution is .43 and the standard deviation of the sampling distribution is .05 .

Answer 1

Answer:

The mean of the sampling distribution is 0.46

The standard deviation of the sampling distribution is 0.01

Step-by-step explanation:

We use the central limit theorem to solve this question:

Central Limit Theorem

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

In this question:

$p = 0.46, n = 2000$

So

Mean: $\mu = p = 0.46$

Standard deviation: $s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.46*0.54}{2000}} = 0.01$

The mean of the sampling distribution is 0.46

The standard deviation of the sampling distribution is 0.01