Question

Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data: B: Percent for company 21 11 16 20 5 8 4 22 A: Percent for CEO 18 5 14 22 10 12 1 17 Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 1% level of significance. What is the value of the test statistic? Select one: a. -0.730 b. -0.683 c. 0.683 d. 0.730 e. -0.639

Answer 1

At 0.01 level of significance, the hypotheses are

Here 2 sample test for the paired sample is applicable hence

Rejection region:

Reject Ho if Test statistic>t_0.005=3.499

Test statistic:

Since the sample size is less than 30, hence we will use two-tailed t-tests for two samples.

T=0.68, calculated using excel software, details shown below.

t-Test: Paired Two Sample for Means
	Company	CEO
Mean	13.375	12.375
Variance	53.69642857	48.26785714
Observations	8	8
Pearson Correlation	0.833055387
Hypothesized Mean Difference	0
df	7
t Stat	0.683130051
P(T<=t) one-tail	0.258244776
t Critical one-tail	2.997951567
P(T<=t) two-tail	0.516489552
t Critic;al two-tail	3.499483297

P value:

P value calculated using Excel at 7 degrees of freedom for the two-tailed test is

0.52.

Conclusion:

Since T < t and P value is greater than the level of significance value, therefore we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that both has a different population mean percentage.