A report states that 42% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to
Within 4% with 95% confidence?
A) 293
B) 585
C) 1170
D) 147

Question

Quizplus · Accepted Answer

To determine the sample size needed to estimate the true proportion with a certain level of confidence and margin of error, we use the formula for sample size in estimating proportions: $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the confidence level (for 95% confidence, $Z = 1.96$), $p$ is the estimated proportion (0.42 in this case), and $E$ is the margin of error (0.04 for 4%). Plugging in the values: $n = \frac{1.96^2 \cdot 0.42 \cdot (1-0.42)}{0.04^2}$, which calculates to approximately 585. Therefore, a sample size of 585 is needed.

A Report States That 42% of Home Owners Had a Vegetable