Concept explainers
An experiment has a single factor with five groups and seven values in each group.
a. How many degrees of freedom are there is determining the among-group variation?
b. How many degrees of freedom are there in determining the within-group variation?
c. How many degrees of freedom are there in determining the total variation?
a.
Determine the value of degrees of freedom for among group variation.
Answer to Problem 1PS
The required value of degrees of freedom is 4.
Explanation of Solution
In a study, among group variation is measured between groups of the data. The degree of freedom for among group variation can be calculated as:
Here,
Hence, the value of degrees of freedom for among group variation is
b.
Determine the value of degrees of freedom for within group variation.
Answer to Problem 1PS
The required value of degrees of freedom is 30.
Explanation of Solution
In a study, within group variation is measured between the data points of each group. The degree of freedom for within group variation can be calculated as:
Here,
Since, there are 5 groups with 7 values each, the total number of data values is:
Substitute
Hence, the value of degrees of freedom for within group variation is
c.
Determine the value of number of degrees for the total variation.
Answer to Problem 1PS
The required value of degrees of freedom is 34.
Explanation of Solution
The degree of freedom for the total variation can be calculated as:
Here,
Hence, the value of degrees of freedom is 34.
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Chapter 11 Solutions
Basic Business Statistics, Student Value Edition
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