If the estimated population proportion is 30 percent based on previous studies, the acceptable error is plus or minus 5 percent, and the z-value for a 95 percent level of confidence is 1.96, the needed sample size is approximately:
A) 323.
B) 187.
C) 36.
D) 212.
E) 554.

Question

Quizplus · Accepted Answer

The sample size needed for estimating a population proportion with a specific level of confidence and margin of error can be calculated using the formula: $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the z-value for the desired confidence level (1.96 for 95%), $p$ is the estimated population proportion (0.30), and $E$ is the acceptable error (0.05). Plugging in the values: $n = \frac{1.96^2 \cdot 0.30 \cdot (1-0.30)}{0.05^2} \approx 323$.

If the Estimated Population Proportion Is 30 Percent Based on Previous