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 25 27 18 6 4 21 37 A: Percent increase for CEO 21 23 24 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: ?d = 0; H1: ?d ≠ 0H0: ?d = 0; H1: ?d > 0 H0: ?d > 0; H1: ?d = 0H0: ?d = 0; H1: ?d < 0H0: ?d ≠ 0; H1: ?d = 0 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that d has an approximately normal distribution.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. 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. A plot of the sampling distribution probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −0.938 is shaded. A plot of the sampling distribution probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 0.938 and 4 is shaded. A plot of the sampling distribution probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −0.938 as well as the area under the curve between 0.938 and 4 are both shaded. A plot of the sampling distribution probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −0.938 and 4 is shaded. (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 the P-value ≤ ?, we reject H0. The data are statistically significant.Since the P-value > ?, we reject H0. The data are not statistically significant. Since the P-value > ?, we fail to reject H0. The data are not statistically significant.Since the P-value ≤ ?, we fail to reject H0. The data are 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 sufficient 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 insufficient 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 increase for company 24 25 27 18 6 4 21 37 A: Percent increase for CEO 21 23 24 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: ?d = 0; H1: ?d ≠ 0H0: ?d = 0; H1: ?d > 0 H0: ?d > 0; H1: ?d = 0H0: ?d = 0; H1: ?d < 0H0: ?d ≠ 0; H1: ?d = 0 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that d has an approximately normal distribution.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. 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. A plot of the sampling distribution probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −0.938 is shaded. A plot of the sampling distribution probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 0.938 and 4 is shaded. A plot of the sampling distribution probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −0.938 as well as the area under the curve between 0.938 and 4 are both shaded. A plot of the sampling distribution probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −0.938 and 4 is shaded. (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 the P-value ≤ ?, we reject H0. The data are statistically significant.Since the P-value > ?, we reject H0. The data are not statistically significant. Since the P-value > ?, we fail to reject H0. The data are not statistically significant.Since the P-value ≤ ?, we fail to reject H0. The data are 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 sufficient 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 insufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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	25	27	18	6	4	21	37
A: Percent increase for CEO	21	23	24	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: ?_d = 0; H₁: ?_d ≠ 0H₀: ?_d = 0; H₁: ?_d > 0 H₀: ?_d > 0; H₁: ?_d = 0H₀: ?_d = 0; H₁: ?_d < 0H₀: ?_d ≠ 0; H₁: ?_d = 0

(b)

What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that d has an approximately normal distribution.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.

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.

A plot of the sampling distribution probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between −4 and −0.938 is shaded.

(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 the P-value ≤ ?, we reject H₀. The data are statistically significant.Since the P-value > ?, we reject H₀. The data are not statistically significant. Since the P-value > ?, we fail to reject H₀. The data are not statistically significant.Since the P-value ≤ ?, we fail to reject H₀. The data are 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 sufficient 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 insufficient to claim a difference in population mean percentage increases for corporate revenue and CEO salary.

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