The following is the information for a completely randomized experimental design involving four treatments,where 12 observations were recorded for each treatment for a total of 48 observations. SST = 210 (Sum of Squares Between Groups); SS Total = 840 (Sum of Squares Total). The computed value of F,or the test statistic,is ________.
A)0.25
B)12.0
C)4.88
D)8.0

Question

Quizplus · Accepted Answer

To calculate F, we need to first find the Sum of Squares within groups (SSW) using the formula SSW = SS Total - SST, which gives us:

SSW = 840 - 210 = 630

Next, we calculate the Mean Square between groups (MSB) and Mean Square within groups (MSW):

MSB = SST / (k-1) = 210 / 3 = 70
MSW = SSW / (N-k) = 630 / (48-4) = 15.75

where k is the number of treatments and N is the total number of observations.

Finally, we compute the F-test statistic as the ratio of MSB to MSW:

F = MSB / MSW = 70 / 15.75 = 4.88

Therefore, the computed value of F is C) 4.88.

The Following Is the Information for a Completely Randomized Experimental