It is estimated that the proportion of Californians in favor of Proposition 5 is between 0.4 and 0.6.The sponsors of the proposition would like to sample Californians and get a 95 percent confidence interval for the true proportion of people in favor of Proposition 5.They want to restrict the error level to 5 percentage points.The required sample size is then
A)400.
B)40.
C)100.
D)1,000.
E)none of the above.

Question

Quizplus · Accepted Answer

The sample size needed for a proportion can be calculated using the formula $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score for the desired confidence level (1.96 for 95%), $p$ is the estimated proportion (0.5 for maximum sample size), and $E$ is the margin of error (0.05 for 5 percentage points). Substituting these values gives $n = \frac{1.96^2 \cdot 0.5 \cdot (1-0.5)}{0.05^2} = 384.16$, which rounds up to 400 for a sample size.

It Is Estimated That the Proportion of Californians in Favor