Question

A simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week. Of the 250 employed individuals​ surveyed, 31 responded that they did work at home at least once per week. Construct a​ 99% confidence interval for the population proportion of employed individuals who work at home at least once per week.

(a) The lower bound is __ and the upper bound is __.

Answer 1

Sample proportion = 31 / 250 = 0.124

99% confidence interval for p is

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

0.124 - 2.576 * sqrt [ 0.124 ( 1 - 0.124) / 250 ] < p < 0.124 + 2.576 * sqrt [ 0.124 ( 1 - 0.124) / 250 ]

0.070 < p < 0.178

99% CI is ( 0.070 , 0.178 )

The lower bound is 0.070 and the upper bound is 0.178