Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package.She plans to use a 95% confidence interval estimate of the proportion of households which prefer the new packages; she will accept a 0.05 error.Previous studies indicate that new packaging has an approximately 70% acceptance rate.The sample size should be at least _______.
A)27
B)59
C)323
D)427
E)500

Question

Quizplus · Accepted Answer

The sample size can be calculated using the formula for estimating a proportion: $n = \frac{Z^2 \times p(1-p)}{E^2}$, where $Z$ is the Z-value for the desired confidence level (1.96 for 95%), $p$ is the estimated proportion (0.7), and $E$ is the margin of error (0.05). Plugging in the values: $n = \frac{1.96^2 \times 0.7(1-0.7)}{0.05^2}$ results in approximately 323.

Catherine Chao, Director of Marketing Research, Is Evaluating Consumer Acceptance