Question: What is the critical F value for a sample of four observations in the numerator and seven in the denominator?
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By "four observations in the numerator and seven in the denominator", I am assuming that you mean there are 4 degrees of freedom for the numerator and 7 degrees of freedom for the denominator. Even when the degrees of freedom for the numerator and denominator are both known, the F- value depends upon the level of significance, alpha.
Some alpha values and the corresponding F- values are given below:
(a) a = 0.10, F = 2.9605
(b) a = 0.05, F = 4.1203
(c) a = 0.02, F = 6.0347
(d) a = 0.01, F = 7.8466.
Hope that this helps!
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