Question

You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p = 0.33. You would like to be 95% confident that your esimate is within 2.5% of the true population proportion. How large of a sample size is required?

n =

Answer #1

Solution :

Given that,

= 0.33

1 - = 1 - 0.33 = 0.67

margin of error = E = 2.5% = 0.025

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2}
= Z_{0.025} = 1.96

Sample size = n = (Z_{/2}
/ E)^{2} *
* (1 -
)

= (1.96 / 0.025)^{2} * 0.33 * 0.67

= 1359

Sample size = 1359

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