Question

3 different types of fertilizer are compared on yield. Each type of fertilizer was applied to 8 different plots. The yield was measured for each plot in and the units are pounds.

The sum of squares within plots

SSW = 7907

and the total sum of squares

SST= 8962

Complete an ANOVA table and test whether there is a difference in yield between the three types of fertilizer.

Answer 1

Null Hypothesis

Alternative Hypothesis H1: At least one of the mean is different

No. of different types of fertilizers ( treatment) is k = 3

No. of plots , n = 8

Total number of yields , N = nk = 8*3 = 24

Anova Table

Source	df	SS	MSS	F
Between Groups	k-1= 3-1 = 2	8962-7907=1055	1055/2 =527.5	527.5/376.5238 =1.401
Within Groups	N-k = 24- 3 = 21	7907	7907/21=376.5238
Total	N-1=24-1 = 23	8962

Degrees of freedom = (2, 21)

Significance Level = 0.05

The critical value of F for (2,21) df at 5% significance level is 3.467

Since F calculated is less than F tabulated. Fail to Reject H0.

Hence, there is no difference in mean yield between the three types of fertilizer.