If we have a sample size of 100 and a population proportion of 0.10,the standard deviation of the sampling distribution of $\hat { p }$ Is ____.
A)10
B)9
C)0.03
D)3
E)90

Question

Quizplus · Accepted Answer

The standard deviation of the sampling distribution of $\hat { p }$ (the sample proportion) is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the population proportion and $n$ is the sample size. Substituting $p = 0.10$ and $n = 100$ gives $\sqrt{\frac{0.10(1-0.10)}{100}} = \sqrt{\frac{0.10(0.90)}{100}} = \sqrt{\frac{0.09}{100}} = \sqrt{0.0009} = 0.03$.

If We Have a Sample Size of 100 and a Population