A study of the pay of corporate chief executive officers (CEOs) examined the inc
ID: 2934332 • Letter: A
Question
A study of the pay of corporate chief executive officers (CEOs) examined the increase in cash compensation of the CEOs of 101 companies, adjusted for inflation, in a recent year. The mean increase in real compensation was x = 7.3%, and the standard deviation of the increases was s = 45%. Is this good evidence that the mean real compensation of all CEOs increased that year?
Because the sample size is large, the sample s is close to the population , so take = 45%.
(a) Sketch the normal curve for the sampling distribution of x when Ho is true. Shade the area that represents the P-value for the observed outcome x = 7.3%. (Do this on paper. Your instructor may ask you to turn in this work.)
(b) Calculate the P-value. (Round your answer to four decimal places.)
(c) Is the result significant at the = 0.05 level? Do you think the study gives strong evidence that the mean compensation of all CEOs went up?
Reject the null hypothesis, there is significant evidence that the mean compensation of all CEOs went up.Reject the null hypothesis, there is not significant evidence that the mean compensation of all CEOs went up. Fail to reject the null hypothesis, there is not significant evidence that the mean compensation of all CEOs went up.Fail to reject the null hypothesis, there is significant evidence that the mean compensation of all CEOs went up.
Ho: = 0 (no increase) Ha: > 0 (an increase)Explanation / Answer
Solution:
From the given information
Sample size n = 101
Sample mean x = 7.3
Standard deviation s=45
= 0
a) t = (7.3-0)/(45/sqrt(101))
t = 1.6303
degree of freedom = n-1 = 100
= 0.05
b) P-value for t = 1.6303 and df=100
= 0.0531
c) Since P-value is greater than '' hence we fail to reject H0
Fail to reject the null hypothesis, there is not significant evidence that the mean compensation of all CEOs went up.
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