The issues surrounding the levels and structure of executive compensation have g

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 Committee (SEC) website, it was determined that the mean and the standard deviation of compensation for the 549 highest paid CEOs in publicly traded U.S. companies is $11.33 million and $10.74 million, respectively. An analyst randomly chooses 36 CEO compensations for 2006. Use Table 1.

Is it necessary to apply the finite population correction factor?

Is the sampling distribution of the sample mean normally distributed?

Calculate the expected value and the standard deviation of the sample mean. (Round your intermediate calculations to 4 decimal places, "expected value" to 2 decimal places and "standard deviation" to 4 decimal places.)

What is the probability that the sample mean is more than $15 million? (Round your intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answer to 4 decimal places.)

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 Committee (SEC) website, it was determined that the mean and the standard deviation of compensation for the 549 highest paid CEOs in publicly traded U.S. companies is $11.33 million and $10.74 million, respectively. An analyst randomly chooses 36 CEO compensations for 2006. Use Table 1.

Explanation / Answer

a)

YES, as the sample size is comparable to the population size.

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b)

YES, as n = 36 > 30.

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c)

Here, s = 10.74, N = 549, n = 36. Hence,

Expected value = 11.33 [ANSWER, in millions]

standard deviation = [s/sqrt(n)]*sqrt[(N-n)/(N-1)] = 3.18320275 [ANSWER]

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d)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    15      
u = mean =    11.33      
          
s = standard deviation =    3.18320275      
          
Thus,          
          
z = (x - u) / s =    1.15      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.15   ) =    0.1251 [ANSWER]

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