In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom df. not in the Student's r table, use the closest df. 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 1864 21 37 8: Percent increase 22 25 27 for company A: Percent increase 21 23 24 14-4 19 15 30 for CEO LAUSE SALT 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-8-A) (a) What is the level of significance? 0.05 State the null and alternate hypotheses ⒸM₂² MgQ; M₁! MO Mg MgO; M₁ MO H₂H0; H₂l My O ⒸM₂² Mg = 0; M₁: Mg > 0 ⒸM₂² Mg = 0; M₁ M₂ TO (b) What sampling distribution will you use? What assumptions are you making? The Student's r. We assume that d has an approximately uniform distribution. The standard normal. We assume that d has an approximately uniform distribution. The Student's r. We assume that of has an approximately normal distribution. The standard normal. We assume that d has an approximately normal 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 0.250P-value < 0.500 0.100 < P-value < 0.250 0.050 < P-value 0.100 0.010 < value < 0.050 OP-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. -2 (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 the A-value sa, we reject M₂. The data are statistically significant. Since the value> a, we fall to reject M. The data are not statistically significant. O Since the P-value > a, we reject M. The data are not statistically significant O Since the P-value sa, we fail to reject H. The data are statistically significant. 0 (e) Interpret your conclusion in the context of the application. Reject M. 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. Reject M. 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 Fall to reject M. 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 reject H. 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. 2