Question

Consider random samples of size 900 from a population with proportion 0.75 . Find the standard error of the distribution of sample proportions. Round your answer for the standard error to three decimal places. standard error

Answer 1

`SE =\sqrt{(p(1-p))/(n)}`

And replacing we got:

`SE=\sqrt{(0.75*(1-0.75))/(900)}= 0.014`

Explanation:

For this case we have the following info given:

`n=900` represent the sample size selected

`p = 0.75` represent the population proportion

We want to find the standard error and we can use the distribution for the sample proportion and for this case since the sample size is large enough and we satisfy np>10 and n(1-p) >10 we have:

`\hat p \sim N (p,\sqrt{(p(1-p))/(n)})`

And the standard error is given;

`SE =\sqrt{(p(1-p))/(n)}`

And replacing we got:

`SE= \sqrt{(0.75* (1-0.75))/(900)}= 0.014`