Question

1. Given: F(1,25). What is N?

2. Given: F_(5,25). What is k?

3. Given: F_(2,25). What is F_(crit) for alpha = .01?

4. If the test statistic (the calculated F ratio) is 10 and the error variance is 5, what is the treatment variance?

5. If the treatment Sum of Squares is 400, and k=5, what is the treatment variance?

6. What is the table value for F_(11,46) when alpha = .05?

7. What is the lowest possible value for the F statistic?

Answer 1

(1) df1 = k - 1 = 1. therefore k = 2

df2 = N - k = 25

Therefore N = 25 + k = 25 + 2 = 27

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(2) df1 = k - 1 = 5

Therefore k = 5 + 1 = 6

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(3) Using F tables for df1 = 2, df2 = 25, at = 0.01, the F critical value = 5.568

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(4) F Stat = Treatment Variance / Error Variance

Treatment Variance = F Stat * Error Variance = 10 * 5 = 50

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(5) The Treatment Variance = Treatment Sum of squares / df1

df1 = k - 1 = 5 - 1 = 4

Therefore Treatment Variance = 400 / 4 = 100

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(6) Using F tables for df1 = 11, df2 = 46, at = 0.05, the F critical value = 2.004

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(7) The least possible value of the F statistic is 0.

The F statistic can never be negative and it ranges from 0 to infinity

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