A survey of 800 women shoppers found that 17% of them shop on impulse. What is the 98% confidence interval for the true proportion of women shoppers who shop on
Impulse?
A) $0.139

Question

A survey of 800 women shoppers found that 17% of them shop on impulse. What is the 98% confidence interval for the true proportion of women shoppers who shop on
Impulse? 
A) $0.139 < p < 0.201$
B) $0.136 < p < 0.204$
C) $0.167 < p < 0.173$
D) $0.144 < p < 0.196$

Quizplus · Accepted Answer

To calculate the 98% confidence interval for the proportion of women shoppers who shop on impulse, we use the formula for the confidence interval of a proportion: $\hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $\hat{p}$ is the sample proportion, $Z_{\alpha/2}$ is the Z-score corresponding to the confidence level, and $n$ is the sample size. Given $\hat{p} = 0.17$ (17%) and $n = 800$, and knowing that the Z-score for a 98% confidence level is approximately 2.33, we calculate the margin of error and add/subtract it from the sample proportion to find the confidence interval. The calculation yields the interval $0.139 < p < 0.201$, which matches choice A.

A Survey of 800 Women Shoppers Found That 17% of Them