Question

The issues surrounding the levels and structure of executive compensation have gained added prominence in the wake of the financial crisis that erupted in the fall of 2008. Based on the 2006 compensation data obtained from the Securities and Exchange Commission (SEC) website, it was determined that the mean and the standard error of compensation for the 582 highest paid CEOs in publicly traded U.S. companies are $12.01 million and $11.38 million, respectively. An analyst randomly chooses 31 CEO compensations for 2006 a. Is it necessary to apply the finite population correction factor? b. Is the sampling distribution of the sample mean approximately normally distributed? c. Calculate the expected value and the standard error of the sample mean. d. What is the probability that the sample mean is more than $17 million?

a. Is it necessary to apply the finite population correction factor?

b. Is the sampling distribution of the sample mean approximately normally distributed?

c. Calculate the expected value and the standard error of the sample mean.

d. What is the probability that the sample mean is more than $17 million?

Answer 1

Solution:

Given: We are given that the mean and the standard error of compensation for the 582 highest paid CEOs in publicly traded U.S. companies are $12.01 million and $11.38 million, respectively

That is:

N = 582

Population mean =

Population Standard Deviation =

Sample size = n = 31

Part a) Is it necessary to apply the finite population correction factor?

If n/N > 0.05, it is necessary to use the finite population correction factor.

Since n/N = 31 / 582 = 0.0533 > 0.05 , so it is necessary to use the finite population correction factor.

Part b) Is the sampling distribution of the sample mean approximately normally distributed?

Since sample size = n= 31 > 30, so we can assume large sample size and thus using Central limit theorem, sampling distribution of the sample mean approximately normally distributed.

Part c) Calculate the expected value and the standard error of the sample mean.

Expected value of Sample mean =

Standard Error of sample mean is:

Part d) What is the probability that the sample mean is more than $17 million?

Find z score:

Thus we get:

Look in z table for z = 2.4 and 0.04 and find area.

P( Z < 2.44)= 0.9927

Thus