Question

A university would like to estimate the proportion of fans who purchase concessions at the first basketball game of the season. The basketball facility has a capacity of

3,600

and is routinely sold out. It was discovered that a total of

290

fans out of a random sample of

500

purchased concessions during the game. Construct a​ 95% confidence interval to estimate the proportion of fans who purchased concessions during the game.

Answer 1

Sample proportion = 290 / 500 = 0.58

95% confidence interval for p is

- Z/2 * sqrt( ( 1 - ) / n) < p < + Z/2 * sqrt( ( 1 - ) / n)

0.58 - 1.96 * sqrt( 0.58 * 0.42 / 500) < p < 0.58 + 1.96 * sqrt( 0.58 * 0.42 / 500)

0.537 < p < 0.623

95% CI is ( 0.537 , 0.623 )