In a recent survey 376 CEOs of medium and large companies we

In a recent survey, 376 CEOs of medium and large companies were asked whether they possessed an MBA degree. In the s ample, 161 had MBA degrees. Give the lower bound of the 99% confidence interval for the true proportion of ail CEOs who have MBAs. Take all intermediate calculators to three decimal places.

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)=161
Sample Size(n)=376
Sample proportion = x/n =0.428
Confidence Interval = [ 0.428 ±Z a/2 ( Sqrt ( 0.428*0.572) /376)]
= [ 0.428 - 2.576* Sqrt(0.001) , 0.428 + 2.58* Sqrt(0.001) ]
= [ 0.362,0.494]

LOWER BOUND: 0.362