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?

Answer 1

Answer:

Minimum Sample size  'n' = 585

Step-by-step explanation:

Explanation:-

Given Estimate of the population proportion as 58% ( = 0.58)

P = 0.58

Given margin of error, E, to be 4%

M.E = 4 % = 0.04

margin of error of the population proportion is determined by

$M.E = \frac{Z_{\frac{\alpha }{2} }\sqrt{p(1-p)} }{\sqrt{n} }$

Z- score = 1.96

$0.04 = \frac{1.96\sqrt{0.58(1-0.58)} }{\sqrt{n} }$

Cross multiplication , we get

$0.04 \sqrt{n} = 1.96 X 0.4935$

$\sqrt{n} = \frac{0.4935 X 1.96}{0.04} = 24.18$

Squaring on both sides, we get

n = 584.7≅585

Conclusion:-

minimum Sample size  'n' = 585

Answer 2

Answer:

585

Step-by-step explanation: