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What sample size is needed to give a margin of error within plus-or-minus 5% in estimating a population proportion with 90% confidence? Use z-values rounded to three decimal places. Round your answer up to the nearest integer. sample sizeequals the absolute tolerance is +/-5

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JeanaShupp

Answer: 271.

Step-by-step explanation:

When the prior population proportion of success is not available, then the formula to find the sample size is given by :-

[tex]n=00.25(\dfrac{z_{\alpha/2}}{E})^2[/tex]

Given : Significance level : [tex]\alpha: 1-0.90=0.1[/tex]

By using the standard normal distribution table ,

Critical value : [tex]z_{\alpha/2}=1.645[/tex]

Margin of error : [tex]E=0.05[/tex]

Then , the required minimum sample size will be :-

[tex]n=0.25(\dfrac{(1.645)}{0.05})^2=270.6025\approx271[/tex]

Hence, the required minimum sample size is 271.

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