The Labor Department wants to estimate the percentage of fem

The Labor Department wants to estimate the percentage of females in the U.S. labor force. They select a random sample of 525 employment records, and find that 210 of the people are females. The 90% confidence interval is

Solution

CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=210
Sample Size(n)=525
Sample proportion = x/n =0.4
Confidence Interval = [ 0.4 ±Z a/2 ( Sqrt ( 0.4*0.6) /525)]
= [ 0.4 - 1.64* Sqrt(0.0005) , 0.4 + 1.64* Sqrt(0.0005) ]
= [ 0.3649,0.4351]