Question

The following is part of an anova table, which was the result of three treatments and a total of 15 of variationsum ofsquaresdegrees offreedommeansquarefbetween treatments64 within treatments (error)96 total if at a 5% level of significance, we want to determine whether or not the means of the populations are equal, the critical value of f is .

a. 4.75
b. 1.96
c. 19.41
d. 3.16

Answer 1

The critical value of F, at a 5% level of significance for an ANOVA test with 2 and 12 degrees of freedom (between and within treatments, respectively), is approximately 3.89. (option B)

To determine the critical value of F for an ANOVA test at a 5% level of significance, we need to use the degrees of freedom associated with the between-treatments and within-treatments (error) sources of variation.

From the information given:

- Degrees of freedom for Between treatments (numerator): df1 = 3 - 1 = 2

- Degrees of freedom for Within treatments (denominator): df2 = 15 - 3 = 12

Now, we need to consult an F-distribution table or use statistical software to find the critical value of F at a 5% level of significance with df1 = 2 and df2 = 12.

Looking up the values in an F-distribution table or using software, the critical value of F at a 5% level of significance for df1 = 2 and df2 = 12 is approximately 3.89.

Therefore, the correct answer is 3.89. (option B)

The complete question is:

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