Thus, the sample of size n=100 will ensure that the 95% confidence interval for the proportion will have a margin of error 0.08.
The formula to estimate the sample size required to estimate the proportion is
[tex]n = p[/tex] × [tex](1-p)( \frac{z}{E} )^{2}[/tex]
where p is the proportion of success, z is the Zα/2 and E is the margin of error.
Given that p=0.21 and the margin of error E=0.08. The confidence coefficient is 0.95. Assume that the proportion is p=0.21.
The critical value of Z is Zα/2=1.96
The minimum sample size required to estimate the proportion is
[tex]n = p[/tex] × [tex](1-p)( \frac{z}{E} )^{2}[/tex]
= [tex]0.21[/tex] × [tex](1-0.21)[/tex] [tex](\frac{1.96}{0.08} )^{2}[/tex]
= 0.21 × 0.79 × 600.25
= 99.581
≈ 100
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