Use the given data to find the minimum sample size required to estimate the population proportion.
-$$\text { Margin of error: } 0.028 \text {; confidence level: } 99 \% ; \hat { p } \text { and } \hat { q } \text { unknown }$$

A) 2115
B) 2223
C) 1939
D) 1116

Question

Use the given data to find the minimum sample size required to estimate the population proportion.
-$$\text { Margin of error: } 0.028 \text {; confidence level: } 99 \% ; \hat { p } \text { and } \hat  { q } \text { unknown }$$

A) 2115
B) 2223
C) 1939
D) 1116

Quizplus · Accepted Answer

The minimum sample size required to estimate the population proportion is given by the formula:$$n = \frac{z^2 \hat{p} \hat{q}}{e^2}$$where:* z is the z-score corresponding to the desired confidence level* p is the estimated population proportion* q is the estimated population proportion* e is the margin of errorIn this case, we are given the following information:* Margin of error: 0.028* Confidence level: 99%* p and q are unknownWe can use the z-score table to find the z-score corresponding to a 99% confidence level. The z-score for a 99% confidence level is 2.576.We can estimate p and q using the sample mean and sample proportion. However, since we do not have any sample data, we will use the conservative estimate of p = q = 0.5.Plugging these values into the formula, we get:$$n = \frac{2.576^2 	imes 0.5 	imes 0.5}{0.028^2} = 2115.26$$Rounding up to the nearest whole number, we get a minimum sample size of 2116.Therefore, the correct answer is A.