The two intervals 0261 0519 and 0227 0553 are confidence int

The two intervals (0.261, 0.519) and (0.227, 0.553) are confidence intervals for a population proportion constructed using the same sample data.

(a) What is the sample proportion?

(b) One of the intervals is a 95% confidence interval; the other interval is a 99% confidence interval. Which is which? How do you know?

Solution

The two intervals (0.261, 0.519) and (0.227, 0.553) are confidence intervals for a population proportion constructed using the same sample data.

(a) What is the sample proportion?

sample proportion = (0.261+0.519)/2 =0.39

or sample proportion = (0.227+0.553)/2 =0.39

(b) One of the intervals is a 95% confidence interval; the other interval is a 99% confidence interval. Which is which? How do you know?

99% confidence interval = p±2.576*se

95% confidence interval = p±1.96*se

99% confidence interval is wider than 95% confidence interval.

99% confidence interval = (0.227, 0.553)

95% confidence interval= (0.261, 0.519)