Question

. A random sample of 20 managers was taken, and they were asked whether or not they usually take work home. The responses of these managers are given below, where Yes indicates they usually take work home and No means they do not.

Yes      No       Yes      Yes      Yes      No       No       Yes      No       Yes

Yes      Yes      Yes      Yes      Yes      No       Yes      Yes      No       Yes

1. Find a point estimator for the proportion of all managers who take work home.
2. Construct a 95% confidence interval for the percentage if all managers who take work home. (Round your answer to 3 decimal places.)
3. Interpret the interval obtained in (b).

Answer 1

Part a)

Point Estimate p̂ = X / n = 14/20 = 0.7

Part b)

p̂ ± Z(α/2) √( (p * q) / n)
0.7 ± Z(0.05/2) √( (0.7 * 0.3) / 20)
Z(α/2) = Z(0.05/2) = 1.96
Lower Limit = 0.7 - Z(0.05) √( (0.7 * 0.3) / 20) = 0.499
upper Limit = 0.7 + Z(0.05) √( (0.7 * 0.3) / 20) = 0.901
95% Confidence interval is ( 0.499 , 0.901 )
( 0.499 < P < 0.901 )

Part c)

We are 95% confident that true population proportion of all managers who take work home lies within the interval  ( 0.499 , 0.901 ).