Question

A simple random sample of 400 persons is taken to estimate the percentage of women in the Boston Teacher's Union whose total membership is 8000. Of those surveyed, 273 teachers are females. We can be 95 percent confident that between...……. percent and ...............percent of the teachers in the union are females.

Answer 1

Sample proportion = 273 / 400 = 0.68

95% confidence interval for p is

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

0.68 - 1.96 * sqrt( 0.68 * 0.32 / 400) < p< 0.68 + 1.96 * sqrt( 0.68 * 0.32 / 400)

0.634 < p < 0.726

We can be 95% confident that between 63.4% and 72.6% pf the teachers in the union are females.