Question

Find the minimum sample size you should use to assure that your estimate of P will be within the required margin of error around the population p. Margin of error: 0.02; confidence interval: 95%; from a prior study, P is estimated by the decimal equivalent of 57%

Answer 1

Answer on Question #48383 – Math - Statistics and Probability

Find the minimum sample size you should use to assure that your estimate of $P$ will be within the required margin of error around the population $p$. Margin of error: 0.02; confidence interval: 95%; from a prior study, $P$ is estimated by the decimal equivalent of 57%

Solution

Confidence interval for population proportion is

$$\text{Sample proportion} \pm \text{Margin of error}.$$ $$\text{Margin of error} = z - \text{score for } 95\% \text{ confidence} \cdot \text{Standard error of } p.$$ $$0.02 = 1.96 \cdot \sqrt{\left(\frac{0.57 \cdot 0.43}{n}\right)},$$

where Standard error of $p$ is $\sqrt{\frac{p(1 - p)}{n}}$.

$$n = 0.57 \cdot 0.43 \cdot \left(\frac{1.96}{0.02}\right)^2 = 235.$$

Therefore the minimum sample size, that can be used, is $n = 235$.

Answer: 235.

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