Question

Based on the random sample of n=800 observations, we have obtained a sample proportion p(bar =0.44. the goal is to test: h(0: p?0.48 h9a: p<0.48 what is the standard error (?(p? rounded to four decimal places

Answer 1

The standard error of a distribution of sample proprtions is defined as the standard deviation of the distribution and is symbolized by
$SE(\hat{p})$
and is calculated by the formula
$SE(\hat{p})= \sqrt{ \frac{p(1-p)}{n} }$.

Given a random sample of n = 800 observations and a sample proportion p = 0.44.

To test:
$H_0:\hat{p}\ \textgreater \ 0.48 \\ H_a:\hat{p}\ \textless \ 0.48$

The standard error rounded to four decimal places is given by:
$SE(\hat{p})= \sqrt{ \frac{0.44(1-0.44)}{800} } \\ \\ = \sqrt{ \frac{0.44(0.56)}{800} } = \sqrt{ \frac{0.2464}{800} } \\ \\ = \sqrt{0.000308} =\bold{0.0175}$