Professor York randomly surveyed 240 students at Oxnard University and found that 150 of the students surveyed watch more than 10 hours of television weekly. Develop a 95 percent confidence interval to estimate the true proportion of students who watch more than 10 hours of television each week. The confidence interval is:
A).533 to .717
B).564 to .686
C).552 to .698
D).551 to .739

Question

Quizplus · Accepted Answer

The correct 95% confidence interval can be calculated using the formula for a proportion confidence interval: $CI = \hat{p} \pm Z * \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $\hat{p}$ is the sample proportion, $Z$ is the Z-score for the desired confidence level (1.96 for 95%), and $n$ is the sample size. Here, $\hat{p} = \frac{150}{240} = 0.625$, $n = 240$, and using the formula, the confidence interval is approximately 0.564 to 0.686.

Professor York Randomly Surveyed 240 Students at Oxnard University and Found