# ANOVA, Freedom For Method, Error and Total,

1. In a one-way ANOVA, there are three treatments with n1 = 6, n2 = 6 and n3 = 5. The rejection region for this test at the 5% level of significance is:

A. F > 4.86

B. F > 3.74

C. F > 4.97

D. F > 3.81

2. The following data show samples of three chain stores in three different locations in one town and the amount of dollars spent per customer per visit.

Store A Store B Store C

30 42 30

14 28 14

22 20 20

18 35 16

26 49 15

25 28

An analysis of variance was performed on these data, resulting in the ANOVA table below. Consider these data and answer the questions that follow.

Source df SS MS

Method 682.79

Error 989.00

Total Critical value = 3.74

a. Fill in the degrees of freedom for Method, Error and Total.

b. Calculate and fill in the Mean Square figures for Method and Error.

c. Calculate the F* statistic for this ANOVA.

d. Summarize your conclusions and results of the test.

3. In a one-way ANOVA, if the test is conducted and the null hypothesis is rejected, what does this indicate?

A. The normal distribution should have been used instead of the F-distribution to determine the critical values of the test

B. All population means are different from one another.

C. At least one of the population means are different

D. All the population means are equal.

4. Choose a variable and collect data for at least three different groups (samples). Compare the means of the three groups using the one-way ANOVA technique. Display all data and show all work. Complete the following:

a. Write a brief statement of the purpose of the study

b. Define the population that is being studied.

c. State how the sample was selected from the population.

d. What α value did you use?

e. State the hypotheses.

f. What was F test value?

g. State the decision that was made based upon the test value.

h. Summarize the results of the study and decision.

You may obtain raw data from the random number table in the appendix section of your text or from any other sources, including sources on the World Wide Web.

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#### Solution Summary

A series of statistical questions is completed.