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 = 200 (Sum of Squares Due to Treatments) SST = 800 (Total Sum of Squares) The mean square due to error (MSE) is a. 600. b. 10. c. 50. d. 200.

Answer 1

Answer:  b. 10

Step-by-step explanation:

Given : In a completely randomized experimental design, total treatments : k= 5

Number of observations : n= 65

Sum of Squares Due to Treatments :  SSTR = 200

Total Sum of Squares : SST = 800

Degree of freedom for SSTR (Sum of Squares Due to Treatments) = n-k

= 65-5 = 60

Sum of squares within treatments : SSE =  SST-  SSTR

=800-200= 600

Then, the mean square due to error will be :

$MSE=\dfrac{SSE}{df}\\\\=\dfrac{600}{60} =10}$

Hence, the mean square due to error (MSE) is 10.

Thus , the correct option is b. 10