Question

A survey of 200 working adults says that 138 of these adults have children.

1. Determine the best point estimate for the true proportion of working adults that have children.

2. Construct a 95% confidence interval for the true proportion of working adults that have children

Answer 1

Part a)

p̂ = X / n = 138/200 = 0.69

Part b)
p̂ ± Z(α/2) √( (p * q) / n)
0.69 ± Z(0.05/2) √( (0.69 * 0.31) / 200)
Z(α/2) = Z(0.05/2) = 1.96
Lower Limit = 0.69 - Z(0.05) √( (0.69 * 0.31) / 200) = 0.6259
upper Limit = 0.69 + Z(0.05) √( (0.69 * 0.31) / 200) = 0.7541
95% Confidence interval is ( 0.6259 , 0.7541 )
( 0.6259 < P < 0.7541 )