Answered: Employee A random sample of companies…

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

Employee A random sample of companies in electric utilities (I), financial services (II), and food processing (III) gave the following information regarding annual profits per employee (units in thousands of dollars).

I	II	III
49.1	55.6	39.0
43.4	25.0	37.3
32.9	41.3	10.8
27.8	29.9	32.5
38.3	39.5	15.8
36.1		42.6
20.2

Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the three types of companies? Use a 1% level of significance. Assume that the distributions are normal and have approximately the same population standard deviation.

What is the level of significance? State the null and alternate hypotheses.
Find SS_TOT, SS_BET, and SS_W and check that SS_TOT = SS_BET + and SS_W. Find d.f._BET, d.f._W, MS_BET and MS_W. Find the value of the sample test statistic F (F ratio). What are the degrees of freedom?
Find (or estimate) the P-value of the sample test statistic.
Based on your answers in parts (1), (2), and (3), will you reject or fail to reject the null hypothesis?
Make a summary table for your ANOVA test.

Expert Solution

Step 1

Part 1:

The level of significance is 0.01.

The null and alternate hypothesis are,

H0: μ₁ = μ₂ = μ₃= 0

H1: at least one μ_i≠ 0

We reject the null hypothesis if F-value > F-critical value.

We perform ANOVA using the step by step procedure in excel as below:

Enter the data into excel sheet.
Go to Data > Data Analysis > Anova: Single factor > Click OK.
Enter the input range and other values as given in the dialogue below and click OK.

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