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{ (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{ (0.44(1-0.44))/(800) } \\ \\ = \sqrt{ (0.44(0.56))/(800) } = \sqrt{ (0.2464)/(800) } \\ \\ = √(0.000308) =\bold{0.0175}`