A random sample of 340 people in Chicago showed that 66 listened to WJKT-1450, a radio station in South Chicago Heights. Based on this information, what is the upper limit for the 95 percent confidence interval estimate for the proportion of people in Chicago that listen to WJKT-1450?
A) 1.96
B) Approximately 0.0009
C) About 0.2361
D) About 0.2298

Question

Quizplus · Accepted Answer

To find the upper limit of the 95% confidence interval for the proportion of people in Chicago that listen to WJKT-1450, we first calculate the sample proportion (p̂) and then use the formula for the confidence interval: p̂ ± Z*(√[p̂(1-p̂)/n]), where Z is the Z-score for the desired confidence level (1.96 for 95%), p̂ is the sample proportion, and n is the sample size. The sample proportion p̂ = 66/340 ≈ 0.1941. Plugging into the formula: 0.1941 ± 1.96*√[0.1941(1-0.1941)/340], the upper limit is approximately 0.2361.

A Random Sample of 340 People in Chicago Showed That