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 B, 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 increasefor company 24 23 27 18 6 4 21 37 A: Percent increasefor CEO 21 27 20 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. H0: μd = 0; H1: μd < 0H0: μd = 0; H1: μd > 0 H0: μd ≠ 0; H1: μd = 0H0: μd = 0; H1: μd ≠ 0H0: μd > 0; H1: μd = 0 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that d has an approximately uniform distribution.The standard normal. We assume that d has an approximately normal distribution. The Student's t. We assume that d has an approximately uniform distribution.The Student's t. 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. P-value > 0.5000.250 < P-value < 0.500 0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-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 α? Since the P-value ≤ α, we reject H0. The data are statistically significant.Since the P-value ≤ α, we fail to reject H0. The data are statistically significant. Since the P-value > α, we reject H0. The data are not statistically significant.Since the P-value > α, we fail to reject H0. The data are not statistically significant. (e) Interpret your conclusion in the context of the application. Reject H0. 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 H0. 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 H0. 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.Fail to reject H0. 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.
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 B, 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 increasefor company 24 23 27 18 6 4 21 37 A: Percent increasefor CEO 21 27 20 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. H0: μd = 0; H1: μd < 0H0: μd = 0; H1: μd > 0 H0: μd ≠ 0; H1: μd = 0H0: μd = 0; H1: μd ≠ 0H0: μd > 0; H1: μd = 0 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that d has an approximately uniform distribution.The standard normal. We assume that d has an approximately normal distribution. The Student's t. We assume that d has an approximately uniform distribution.The Student's t. 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. P-value > 0.5000.250 < P-value < 0.500 0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-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 α? Since the P-value ≤ α, we reject H0. The data are statistically significant.Since the P-value ≤ α, we fail to reject H0. The data are statistically significant. Since the P-value > α, we reject H0. The data are not statistically significant.Since the P-value > α, we fail to reject H0. The data are not statistically significant. (e) Interpret your conclusion in the context of the application. Reject H0. 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 H0. 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 H0. 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.Fail to reject H0. 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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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 B, 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 for company |
24 | 23 | 27 | 18 | 6 | 4 | 21 | 37 |
| A: Percent increase for CEO |
21 | 27 | 20 | 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.
(b) What sampling distribution will you use? What assumptions are you making?
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Find (or estimate) the P-value.
Sketch the sampling distribution and show the area corresponding to the P-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 α?
(e) Interpret your conclusion in the context of the application.
State the null and alternate hypotheses.
H0: μd = 0; H1: μd < 0H0: μd = 0; H1: μd > 0 H0: μd ≠ 0; H1: μd = 0H0: μd = 0; H1: μd ≠ 0H0: μd > 0; H1: μd = 0
(b) What sampling distribution will you use? What assumptions are you making?
The standard normal. We assume that d has an approximately uniform distribution.The standard normal. We assume that d has an approximately normal distribution . The Student's t. We assume that d has an approximately uniform distribution.The Student's t. 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.
P-value > 0.5000.250 < P-value < 0.500 0.100 < P-value < 0.2500.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010
Sketch the sampling distribution and show the area corresponding to the P-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 α?
Since the P-value ≤ α, we reject H0. The data are statistically significant.Since the P-value ≤ α, we fail to reject H0. The data are statistically significant. Since the P-value > α, we reject H0. The data are not statistically significant.Since the P-value > α, we fail to reject H0. The data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
Reject H0. 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 H0. 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 H0. 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.Fail to reject H0. 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.
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