Answered: Using techniques from an earlier…

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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Using techniques from an earlier section, we can find a confidence interval for ?_d. 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

of the differences and the sample standard deviation s_d. If d has a normal distribution or is mound-shaped, or if n ≥ 30, then a confidence interval for ?_d is as follows.

d − E < ?_d < d + E

where

E = t_c

s_d

c = confidence level (0 < c < 1)

t_c = critical value for confidence level c and d.f. = n − 1

B: Percent increase for company	16	24	28	18	6	4	21	37
A: Percent increase for CEO	22	14	18	14	−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 limitupper 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 ?_d = 0 from the null hypothesis is in the 95% confidence interval, do not reject H₀ 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 ?_d = 0 from the null hypothesis is not in the 95% confidence interval, reject H₀ at the 5% level of significance. The data indicate a difference in population mean percentage increases between company revenue and CEO salaries. Since ?_d = 0 from the null hypothesis is in the 95% confidence interval, reject H₀ 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 ?_d = 0 from the null hypothesis is not in the 95% confidence interval, do not reject H₀ at the 5% level of significance. The data indicate a difference in population mean percentage increases between company revenue and CEO salaries.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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