In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'sttable, use the closestd.f. that issmaller. In some situations, this choice ofd.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer.

Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at rowB, the annual company percentage increase in revenue, versus rowA, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data:

B: Percent increase

for company 26 23 27 18 64 21 37

A: Percent increase for CEO 23 25 22 14 41 9 15 30

Do these data indicate that the population mean percentage increase in corporate revenue (rowB) is different from the population mean percentage increase in CEO salary? Use a 5% level of significance. (Letd=BA.)(a) What is the level of significance?

State the null and alternate hypotheses.

H₀:_d0;H₁:_d= 0

H₀:_d= 0;H₁:_d> 0

H₀:_d= 0;H₁:_d0

H₀:_d= 0;H₁:_d< 0

H₀:_d> 0;H₁:_d= 0

(b) What sampling distribution will you use? What assumptions are you making?

The standard normal. We assume thatdhas an approximately uniform distribution.

The standard normal. We assume thatdhas an approximately normal distribution.

The Student'st. We assume thatdhas an approximately uniform distribution.

The Student'st. We assume thatdhas an approximately normal distribution.

What is the value of the sample test statistic? (Round your answer to three decimal places.)

(c) Find (or estimate) theP-value.

P-value > 0.500

0.250 <P-value < 0.500

0.100 <P-value < 0.250

0.050 <P-value < 0.100

0.010 <P-value < 0.050

P-value < 0.010

Sketch the sampling distribution and show the area corresponding to theP-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

Since theP-value, we fail to rejectH₀. The data are statistically significant.

Since theP-value >, we rejectH₀. The data are not statistically significant.

Since theP-value >, we fail to rejectH₀. The data are not statistically significant.

Since theP-value, we rejectH₀. The data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to rejectH₀. At the 5% level of significance, the evidence is insufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

RejectH₀. At the 5% level of significance, the evidence is sufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

Fail to rejectH₀. At the 5% level of significance, the evidence is sufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

RejectH₀. At the 5% level of significance, the evidence is insufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.