Question

An agricultural scientist decides to compare the effect three fertilizers have on the heights of a certain type of plant. For each fertilizer (A, B, and C), plants are fertilized and otherwise treated identically. After four weeks, the heights in centimeters for each plant is measured. The means are given below. Fertilizer A: 26, 28, 30 Fertilizer B: 17, 21, 16 Fertilizer C: 18, 19, 17, 18 Complete the analysis of variance table. Degrees of Freedom Sum of Squares Mean Square f P value Source of Variation Treatments Error Total

Answer 1

The Analysis of Variance Table is completed as follows:

Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	f	P value
Treatments	2	210	210/2=105	105/3.429=30.624	0.0003
Error	7	24	24/7=3.429
Total	9	234

The entries in the Analysis of Variance Table are calculated as follows:

From the given data, the following Table is calculated:

	Fertilizer A	Fertilizer B	Fertilizer C
n	3	3	4
Sum	84	54	72
Mean	28	18	18
$\sum X^{2}_{ij}$	2360	986	1298
Std. Dev.	2	2.646	0.816
SS	8	14	2

Xij = 84 +54 + 72 = 210

Σx? 2360 + 986 + 1298 = 4644 20

(ΣΧ;)? SStotal = Σx? 4644 2102 10 = 234 n

S Streatment 234 - 24 = 210

210 M Streatment 105 2

Test Statistic F is given by:

F = 105 3.429 30.624

By Technology,

P - Value = 0.0003