Homework Sourse29 Executive compensation has risen dramatically beyond the
29. Executive compensation has risen dramatically beyond the rising levels of an average worker’s wage over the years. Sarah is an MBA student who decides to use her statistical skills to estimate the mean CEO compensation in 2010 for all large companies in the United States. She takes a random sample of six CEO compensations.
Firm Compensation (in $ millions)
Intel 8.2
Coca-Cola 2.76
Wells Fargo 6.57
Caterpillar 3.88
McDonald’s 6.56
U.S. Bancorp 4.1
a. How will Sarah use the above information to provide a 90% confidence interval of the mean CEO compensation of all large companies in the United States?
b. What assumption did Sarah make for deriving the interval estimate?
c. How can Sarah reduce the margin of error reported in the above interval estimate?
Solution
a)
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=5.345
Standard deviation( sd )=2.0739
Sample Size(n)=6
Confidence Interval = [ 5.345 ± t a/2 ( 2.0739/ Sqrt ( 6) ) ]
= [ 5.345 - 2.015 * (0.847) , 5.345 + 2.015 * (0.847) ]
= [ 3.639,7.051 ]
b)
We are 90% confident that the mean CEO compensation of all large companies in the United States
is lies in iterval [3.639,7.051]
c)
By increasing the sample size or Decreasing the confidence interval
