Question

A prior study determined the point estimate of the population proportion as 58% ( = 0.58). The analysts decide to conduct a second study on the same topic and would like its margin of error, E, to be 4% when its confidence level is 95% (z*-score of 1.96). What is the minimum sample size that should be used so the estimate of will be within the required margin of error of the population proportion? n = (1 – ) • 12 23 585 808

Answer 1

585

Explanation:

just took test

Answer 2

The minimum sample size required for a test with a confidence interval of
`100(1 - \alpha )%` with a z-score of
`z_( \alpha /2)` and margin of error of E and a population proportion of p is given by:


`n= (p(1-p)z_( \alpha /2)^2 \alpha )/(E^2)`

Given p = 58% = 0.58, E = 4% = 0.04,
`z_( \alpha /2)=1.96`

Therefore,


`n= (0.58(1-0.58)(1.96)^2)/(0.04^2) \\ \\ = (0.58(0.42)(3.8416))/(0.0016) = (0.93581376)/(0.0016) \\ \\ =584.88=585`