Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package.She randomly selects a sample of 200 households.Forty households prefer the new package to all other package designs.The 90% confidence interval for the population proportion is _________.
A)0.199 to 0.201
B)0.153 to 0.247
C)0.164 to 0.236
D)0.145 to 0.255
E)0.185 to 0.275

Question

Quizplus · Accepted Answer

To calculate the 90% confidence interval for the population proportion, we use the formula for the confidence interval of a proportion: $$p \pm Z \sqrt{\frac{p(1-p)}{n}}$$, where $p$ is the sample proportion, $Z$ is the Z-score corresponding to the confidence level, and $n$ is the sample size. Here, $p = \frac{40}{200} = 0.2$, $n = 200$, and for a 90% confidence level, $Z \approx 1.645$. Plugging these values into the formula gives us the interval $0.2 \pm 1.645 \sqrt{\frac{0.2(0.8)}{200}}$, which calculates to approximately $0.153$ to $0.247$.

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