What is the conference interval.

Question

A sample of 300 high school seniors found that 195 of them took the SAT more than once. Find the 99% confidence interval for the proportion of all high school seniors who took the SAT more than once.

Answer 1

The sample size is greater than or equal to 30 so The Standard Normal Distribution will be used.

The sample proportion who took the SAT more than once is p-bar = 195/300 or 0.65 and the proportion who did not take the SAT more than once is q-bar = 105/300 or 0.35.

The Estimated Standard Error of the proportion is √((p-bar)(q-bar)/n) or √((0.65)(0.35)/300) ≈ 0.0275. The z value for the 99% Confidence Level is 2.58.

The Lower Limit of the 99% Confidence Interval is p-bar – z√((p-bar)(q-bar)/n) or 0.65 – 2.58(0.0275) ≈ 0.579.

The Upper Limit of the 99% Confidence Interval is p-bar + z√((p-bar)(q-bar)/n) or 0.65 + 2.58(0.0275) ≈ 0.721.

The 99% Confidence Interval sought is then (0.579,0.721).