Data from a randomized block design are shown in the following table.
With $\alpha$ = 0.05,the observed F value for the blocking effects null hypothesis is__.
A) 0.37
B) 5.14
C) 1.17
D) 2.33
E) 2.00

Question

Data from a randomized block design are shown in the following table.  
With $\alpha$ = 0.05,the observed F value for the blocking effects null hypothesis is__.
A) 0.37 
B) 5.14 
C) 1.17 
D) 2.33 
E) 2.00

Quizplus · Accepted Answer

To find the observed F value for the blocking effects null hypothesis, we need to calculate the mean square for blocks (MS_blocks) and the mean square error (MS_error). 
MS_blocks = SS_blocks / df_blocks = 4126.7 / 2 = 2063.35 
MS_error = SS_error / df_error = 2406.7 / 18 = 133.7 
The F value for blocking effects is then: 
F_blocks = MS_blocks / MS_error = 2063.35 / 133.7 = 15.44 
Compared to the critical value for F1F1F1S1F1F1F10 = 0.05 (3.59), we can see that F_blocks is not significant. Therefore, the null hypothesis for blocking effects cannot be rejected. The answer is C, which corresponds to the F value of 1.17.

Data from a Randomized Block Design Are Shown in the Following