A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees from each firm: How many months did you work before receiving a raise in salary? Using the following ANOVA table, is there a difference in the mean number of months before receiving a raise among the four firms? Use the 0.01 level of significance. Analysis of Variance Source df SS MS F p Factor 3 25.89 8.63 4.27 0.031 Error 11 22.21 2.02 Total 14 48.10 a. What are the null and alternate hypotheses? H0: (μ1 > μ2 > μ3 > μ4 or μ1 = μ2 = μ3 = μ4 or μ1 ≠ μ2 ≠ μ3 ≠ μ4 or Treatment means are not all equal) _____ H1: (μ1 > μ2 > μ3 > μ4 or μ1 = μ2 = μ3 = μ4 or μ1 ≠ μ2 ≠ μ3 ≠ μ4 or Treatment means are not all equal) _ b. What is the test statistic? (Round your answer to 2 decimal places.)The test statistic is _c. What is the p-value? (Round your answer to 3 decimal places.)The p-value is d. What is your decision regarding the null hypothesis?Decision: (Reject or Do Not Reject)n_ H0e. Interpret the result. There is (a difference or no difference) ______ in the mean number of months before receiving a raise among the four firms.

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

A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees from each firm: How many months did you work before receiving a raise in salary? Using the following ANOVA table, is there a difference in the mean number of months before receiving a raise among the four firms? Use the 0.01 level of significance.

Source	df	SS	MS	F	p
Analysis of Variance
Factor	3	25.89	8.63	4.27	0.031
Error	11	22.21	2.02
Total	14	48.10

a. What are the null and alternate hypotheses?

H₀: (μ₁ > μ₂ > μ₃ > μ₄ or μ₁ = μ₂ = μ₃ = μ₄ or μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ or Treatment means are not all equal) ___________

H₁: (μ₁ > μ₂ > μ₃ > μ₄ or μ₁ = μ₂ = μ₃ = μ₄ or μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ or Treatment means are not all equal) ___________

b. What is the test statistic? (Round your answer to 2 decimal places.)

The test statistic is _________

c. What is the p-value? (Round your answer to 3 decimal places.)

The p-value is ________

d. What is your decision regarding the null hypothesis?

Decision: (Reject or Do Not Reject)n_________ H₀

e. Interpret the result.

There is (a difference or no difference) __________ in the mean number of months before receiving a raise among the four firms.

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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