Question

According Two data from the 2010 United States Census 83.7% of Americans lived in the metropolitan area suppose maria researcher takes a random sample of 125 Americans and find that 98 live in the Metropolitan area let P hat represent the sample proportion of Americans that live in a metropolitan area what are the mean and standard deviation of the sampling distribution of P hat provide your answer rounded to three decimal places

Answer 1

Mean is 83.7%

And, the standard deviation is 0.033

Explanation:

The computation of the mean and the standard deviation is as follows:

Let us assume the P be the sample proportion

Mean is 83.7%

And, the standard deviation is

`= \sqrt{(p(1-p))/(n) } \\\\=\sqrt{(0.837(1-0.837))/(125) }`

= 0.033