In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information.
SSTR = 300 (Sum of Squares Due to Treatments)
SST = 800 (Total Sum of Squares)

If, at a 5% level of significance, we want to determine whether or not the means of the five populations are equal, the critical value of F is
A) 2.53.
B) 19.48.
C) 4.98.
D) 5.69.

Question

In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). Also, the design provided the following information. ​
SSTR = 300 (Sum of Squares Due to Treatments)
SST = 800 (Total Sum of Squares)
​
If, at a 5% level of significance, we want to determine whether or not the means of the five populations are equal, the critical value of F is
A) 2.53.
B) 19.48.
C) 4.98.
D) 5.69.

Quizplus · Accepted Answer

The critical value of F is determined by the F-distribution table using the degrees of freedom for the numerator (k-1 = 5-1 = 4) and the denominator (N-k = 65-5 = 60) at a 5% significance level. The critical value for F(4, 60) at 0.05 significance level is approximately 2.53.

In a Completely Randomized Experimental Design Involving Five Treatments, 13