In this problem, assume that the distribution of differences is approximately normal. Note : For degrees of freedom d . f . not in the Student's t table, use the closest d . f . that is smaller . In...

In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'st table, 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	24	25	25	18	6	4	21	37
A: Percent increase for CEO	21	25	22	14	−4	19	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 =B −A.)

(a)What is the level of significance?
=___

State the null and alternate hypotheses.

H
₀: ?_d = 0;H
₁: ?_d ≠ 0H
₀: ?_d = 0;H
₁: ?_d <>H
₀: ?_d ≠ 0;H
₁: ?_d = 0H
₀: ?_d = 0;H
₁: ?_d > 0H
₀: ?_d > 0;H
₁: ?_d = 0

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

A-The standard normal. We assume thatd has an approximately normal distribution.

B-The Student'st. We assume thatd has an approximately uniform distribution.

C-The Student'st. We assume thatd has an approximately normal distribution.

D-The standard normal. We assume thatd has an approximately uniform distribution.

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

=___

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

A-P-value > 0.500

B-0.250 P-value <>

C-0.100 P-value <>

D-0.050 P-value <>

E-0.010 P-value <>

F-P-value <>

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 ??

A-Since theP-value ≤ ?, we fail to rejectH
₀. The data are statistically significant.

B-Since theP-value ≤ ?, we rejectH
₀. The data are statistically significant.

C-Since theP-value > ?, we fail to rejectH
₀. The data are not statistically significant.

D-Since theP-value > ?, we rejectH
₀. The data are not statistically significant.

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

A-Fail to rejectH
₀. 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.

B-RejectH
₀. 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.

C-Fail to rejectH
₀. 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.

D-RejectH
₀. 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.

Jun 09, 2022

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In this problem, assume that the distribution of differences is approximately normal. Note : For degrees of freedom d . f . not in the Student's t table, use the closest d . f . that is smaller . In...

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