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 24 18 20 for company A: Percent increase for CEO USE SALT 27 test statistic = critical value = + 25 19 18 14 6 -4 4 19 21 37 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. Solve the problem using the critical region method of testing. (Let d= B- A. Round your answers to three decimal places.) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Reject the null hypothesis, there is insufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Reject the null hypothesis, there is sufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Fail to reject the null hypothesis, there is insufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? We reject the null hypothesis using the P-value method, but fail to reject using the critical region method. We reject the null hypothesis The conclusions obtained by using both methods are the same. using the critical region method, but fail to reject using the P-value method.
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 24 18 20 for company A: Percent increase for CEO USE SALT 27 test statistic = critical value = + 25 19 18 14 6 -4 4 19 21 37 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. Solve the problem using the critical region method of testing. (Let d= B- A. Round your answers to three decimal places.) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Reject the null hypothesis, there is insufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Reject the null hypothesis, there is sufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Fail to reject the null hypothesis, there is insufficient evidence to claim a difference in population mean percentage increases for corporate revenue and CEO salary. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? We reject the null hypothesis using the P-value method, but fail to reject using the critical region method. We reject the null hypothesis The conclusions obtained by using both methods are the same. using the critical region method, but fail to reject using the P-value method.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:16
In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of
freedom d.f. not in the Student's ttable, 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 24 18 20
for company
A: Percent increase
for CEO
USE SALT
27 25
test statistic =
critical value = +
19
18
14
6
4
19
21 37
15 30
r
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.
Solve the problem using the critical region method of testing. (Let d= B- A. Round your answers to three
decimal places.)
Interpret your conclusion in the context of the application.
Fail to reject the null hypothesis, there is sufficient evidence to claim a difference in population mean
percentage increases for corporate revenue and CEO salary. Reject the null hypothesis, there is
insufficient evidence to claim a difference in population mean percentage increases for corporate
revenue and CEO salary. Reject the null hypothesis, there is sufficient evidence to claim a difference
in population mean percentage increases for corporate revenue and CEO salary. Fail to reject the null
hypothesis, there is insufficient evidence to claim a difference in population mean percentage increases
for corporate revenue and CEO salary.
Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?
We reject the null hypothesis using the P-value method, but fail to reject using the critical region method.
We reject the null hypothesis
The conclusions obtained by using both methods are the same.
using the critical region method, but fail to reject using the P-value method.
Transcribed Image Text:15
Using techniques from an earlier section, we can find a confidence interval for μd. Consider a random
sample of n matched data pairs A, B. Let d= B - A be a random variable representing the difference
between the values in a matched data pair. Compute the sample mean
d
of the differences and the sample standard deviation Sd. If d has a normal distribution or is mound-
shaped, or if n ≥ 30, then a confidence interval for LL is as follows.
d-E< <d+ E
where
E = te
Sd
√n
c= confidence level (0 <c< 1)
te = critical value for confidence level cand d.f. = n-1
B: Percent increase
for company
A: Percent increase
for CEO
USE SALT
20 16 28 18 6 4 21 37
30 26 24 14
upper limit
-4 19 15 30
(a)
Using the data above, find a 95% confidence interval for the mean difference between percentage
increase in company revenue and percentage increase in CEO salary. (Round your answers to two
decimal places.)
lower limit
(b)
Use the confidence interval method of hypothesis testing to test the hypothesis that population mean
percentage increase in company revenue is different from that of CEO salary. Use a 5% level of
significance.
Since μ = 0 from the null hypothesis is in the 95% confidence interval, reject H at the 5% level of
significance. The data do not indicate a difference in population mean percentage increases between
company revenue and CEO salaries. Since μ = 0 from the null hypothesis is in the 95% confidence
interval, do not reject Ho at the 5% level of significance. The data do not indicate a difference in population
O
mean percentage increases between company revenue and CEO salaries. Since μ = 0 from the
null hypothesis is not in the 95% confidence interval, reject Ho at the 5% level of significance. The data
indicate a difference in population mean percentage increases between company revenue and CEO
salaries. Since μ = 0 from the null hypothesis is not in the 95% confidence interval, do not
reject Ho at the 5% level of significance. The data indicate a difference in population mean percentage
increases between company revenue and CEO salaries.
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