Question

6. 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 470 highest paid CEOs in publicly traded U.S. companies are $9.70 million and $9.19 million, respectively. An analyst randomly chooses 38 CEO compensations for 2006. [You may find it useful to reference the z table.]

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

• Yes

• No

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

• Yes

• No

c. Calculate the expected value and the standard error of the sample mean.(Round "expected value" to 2 decimal places and "standard error" to 4 decimal places.)

Expected Value
Standard Error

d. What is the probability that the sample mean is more than $14 million? (Round "z" value to 2 decimal places, and final answer to 4 decimal places.)

Probability

Answer 1

We are given sample mean() = 9.70 and SE() = 9.19

Number of sample chosen n=38

Answer a : Yes

Because the population size is finite and not that much big but sample is not big enough  

Answer b : Yes

Answer c :

From theory we know that the sample average()  has mean μ and variance σ² / n

Expected value = 9.70

Stander Error = = 1.4908

Answer d :

We need to find

Now we have

where

  

= 0.0062