Question

Find the standard deviation for the sampling distribution of the sample proportion with n=75 and n=1500P=0.45

Answer 1

The standard deviation of a sample portion is

$\sigma_{\hat{p}}=\sqrt[]{\frac{pq}{n}}$

Where p = 45 and q = 1 - p.

$q=1-0.45=0.55$

Let's find the standard deviation of the sample n = 75.

$\sigma_{\hat{p}}=\sqrt[]{\frac{0.45\cdot0.55}{75}}\approx0.057$

The standard deviation of the first sample is 0.057.

Repeat the process for n = 1500.

$\sigma_{\hat{p}}=\sqrt[]{\frac{0.45\cdot0.55}{1500}}\approx0.0128$

The standard deviation of the second sample is 0.0128.

Therefore,

• When n = 75, the standard deviation is 0.057.

,

• When n = 1500, the standard deviation is 0.0128.