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A researcher is interested in whether students' GPA differs as a function of area of academic...

A researcher is interested in whether students' GPA differs as a function of area of academic specialization. The researcher obtains the names of all currently enrolled Brooklyn College students. She randomly selects 21 students from each of the following majors:

Group 1: Psychology     Group 2: Biology     Group 3: History     Group 4: Art     Group 5: Education   

n1= 21                             n2= 21                       n3= 21                      n4= 21               n5= 21                

Question 1: What is the critical value for this F-test for α = 0.05?

Question 2: What is the critical value for this F-test for α = 0.01?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

As 21 samples are selected from each group. So, total will be 21+21+21+21 = 84.

So, degrees of freedom for total is df = 84-1 = 83

Now, the degrees of freedom for group ( between) is 5-1 = 4

Within the sum of squares(error) degrees of freedom is 83-4 = 79 .

The critical value of F test at (4,79) degrees of freedom at α = 0.05 is 2.48736595.

The critical value of F test at (4,79) degrees of freedom at α = 0.01 is 3.56632955

Note: - Critical values are collected from F table.

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