According to a hospital administrator,historical records over the past 10 years have shown that 20 percent of the major surgery patients are dissatisfied with after-surgery care in the hospital.A scientific poll based on 400 hospital patients has just been conducted.Sixty-four patients indicated that they were dissatisfied with the after-surgery care.What are the mean and the standard deviation of the sampling distribution of $\hat { p }$?
A)16% and .034%
B)20% and 1.83%
C)20% and 2%
D)20% and .034%
E)20% and 16%

Question

Quizplus · Accepted Answer

The sample proportion can be calculated as:

$\hat{p} = \frac{64}{400} = 0.16 = 16\%$

The standard deviation of the sampling distribution of $\hat{p}$ can be calculated as:

$\sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.2(0.8)}{400}} = 0.02 = 2\%$

Therefore, the mean and standard deviation of the sampling distribution of $\hat{p}$ are 20% and 2%, respectively. The correct answer is (C).

According to a Hospital Administrator,historical Records Over the Past 10 p^\hat { p }p^​

According to a Hospital Administrator,historical Records Over the Past 10 $\hat { p }$