A recent book noted that only 20 of investment managers out

A recent book noted that only 20% of investment managers out perfrom the standard indexes, such as Dow Jones Industrial Average onr the NASDAQ, overa a five year period. A sample of 400 investment managers that had graduated from one of the top 10 Business programs in the country were followed over a 5 year period. 100 of the outperformed the Dow Jones. Let p represent the probability that a random investment manager who graduated from one of the top 10 Business programs will out perform the Dow Jones over a 5 year period.

Based on the sample, a 95% confidence interval for p 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
No. of outperformed the Dow Jones(x)=100
Sample Size(n)=400
Sample proportion = x/n =0.25
Confidence Interval = [ 0.25 ±Z a/2 ( Sqrt ( 0.25*0.75) /400)]
= [ 0.25 - 1.96* Sqrt(0) , 0.25 + 1.96* Sqrt(0) ]
= [ 0.208,0.292]