Here is a question from Kaplan:
A dependent variable is regressed against three independent variables across 25 observations. The regression sum of squares is 119.25, and the total sum of squares is 294.45. The following are the estimated coefficient values and standard errors of the coefficients.
Coefficient Value Standard error 1 2.43 1.4200 2 3.21 1.5500 3 0.18 0.0818
What is the p-value for the test of the hypothesis that all three of the coefficients are equal to zero?
A) lower than 0.025. 
B) Between 0.05 and 0.10. 
C) Between 0.025 and 0.05.
Explanation
This test requires an F-statistic, which is equal to the ratio of the mean regression sum of squares to the mean squared error.
The mean regression sum of squares is the regression sum of squares divided by the number of independent variables, which is 119.25 / 3 = 39.75.
The residual sum of squares is the difference between the total sum of squares and the regression sum of squares, which is 294.45 − 119.25 = 175.20. The denominator degrees of freedom is the number of observations minus the number of independent variables, minus 1, which is 25 − 3 − 1 = 21. The mean squared error is the residual sum of squares divided by the denominator degrees of freedom, which is 175.20 / 21 = 8.34.
The F-statistic is 39.75 / 8.34 = 4.76, which is higher than the F-value (with 3 numerator degrees of freedom and 21 denominator degrees of freedom) of 3.07 at the 5% level of significance and higher than the F-value of 3.82 at the 2.5% level of significance. The conclusion is that the p-value must be lower than 0.025.
Remember the p-value is the probability that lies above the computed test statistic for upper tail tests or below the computed test statistic for lower tail tests.
Question:
I disagree with the highlighted part. If for 5% and 2.5% significance levels the calculated F-stat is bigger than the Critical F-Stat values we should reject the null Hypothesis and conclude that at least one of the coefficients is not 0 therefor - which was not the question of the exercise, therefore the choice A) that p-value should be less than 2.5% is not a correct answer for me here. Could someone please explain, I guess there is something I`m not getting right.
Thanks many times,
Ann