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 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 ?d is as follows. d − E < ?d < d + E where E = tc sd n c = confidence level (0 < c < 1) tc = critical value for confidence level c and d.f. = n − 1 B: Percent increase for company 16 24 8 18 6 4 21 37 A: Percent increase for CEO 18 16 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 limit upper 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 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, 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, 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.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.

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 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 ?d is as follows. d − E < ?d < d + E where E = tc sd n c = confidence level (0 < c < 1) tc = critical value for confidence level c and d.f. = n − 1 B: Percent increase for company 16 24 8 18 6 4 21 37 A: Percent increase for CEO 18 16 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 limit upper 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 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, 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, 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.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.

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Description: 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. Compu

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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	8	18	6	4	21	37
A: Percent increase for CEO	18	16	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 limit upper 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 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, 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, 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.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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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