Data from a randomized block design are shown in the following table:
Using $\alpha$ = 0.05,the critical F value for the treatments null hypothesis is ___.
A)3.59
B)4.76
C)3.98
D)5.14
E)9.89

Question

Data from a randomized block design are shown in the following table:  
Using $\alpha$ = 0.05,the critical F value for the treatments null hypothesis is ___.
A)3.59 
B)4.76 
C)3.98 
D)5.14 
E)9.89

Quizplus · Accepted Answer

To find the critical F value, we need to first calculate the degrees of freedom for treatments (dfT) and error (dfE). For this design, there are two treatments (Factor A and Factor B) and four blocks. Therefore, dfT = number of treatments - 1 = 2 - 1 = 1 and dfE = (number of blocks - 1) x (number of observations per block - 1) = (4 - 1) x (2 - 1) = 3.
Using the F table with dfT = 1 and dfE = 3, and a significance level of 0.05 (alpha = 0.05), we find that the critical F value is 4.76. Therefore, the best choice is B.

Data from a Randomized Block Design Are Shown in the Following