In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f.

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In This Problem Assume That The Distribution Of Differences Is Approximately Normal Note For Degrees Of Freedom D F 1 (34.77 KiB) Viewed 92 times

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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 some situations, this choice of d.f. may increase the P-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 row 8, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose a random sample of companies yielded the following data: B: Percent increase 22 25 25 18 6 4 for company A: Percent increase for CEO 21 37 21 23 22 14 -4 19 15 30 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 5% level of significance. (Let d B-A.) (a) What is the level of significance? State the null and alternate hypotheses. ⒸHo Hd O; H₂ Hd O ⒸHo Hg = 0; H₂H #0 Ho: H0; H₂: M-0 ⒸH₂² Hg = 0; H₁² Hy 20 Hoi Hd = 0; H₁ H₂ <0
(b) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately uniform distribution. O The Student's t. We assume that d 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) the P-value. OP-value> 0.500 O 0.250 < P-value < 0.500 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 0.010< P-value < 0.050 OP-value < 0.010
Sketch the sampling distribution and show the area corresponding to the P-value. -2 0 0 2 2 0 4 e
(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? O Since the P-value > a, we fail to reject Ho. The data are not statistically significant. O Since the P-value sa, we reject Ho. The data are statistically significant. O Since the P-value > a, we reject Ho- The data are not statistically significant. O Since the P-value sa, we fail to reject Ho. The data are statistically significant. (e) Interpret your conclusion in the context of the application. O Fail to reject H₂. 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. O Reject Ho 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. O Fail to reject Ho. 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. Reject Ho. 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.