Question

The following table shows the grain yield of rice at six seeding rates (Mg/ha). This was replicated 4 times. The primary objective is to discover if there is a significant difference among the seeding rates.

	Seeding rate (kg/ha)
Rep	25	50	75	100	125	150
1	5.1	5.3	5.3	5.2	4.8	5.3
2	5.4	6	5.7	4.8	4.8	4.5
3	5.3	4.7	5.5	5	4.4	4.9
4	4.7	4.3	4.7	4.4	4.7	4.1

Run a INITIAL appropriate test at alpha = 0.05

Answer 1

H0: There is no significant difference among the seeding rates.

H1: There is a significant difference among the seeding rates.

Let the los be alpha = 0.05

From the given data, Given n = 4 and k = 6

	Repeatation
	1	2	3	4	Ti.	SS	Ti.^2/n
25	5.1	5.4	5.3	4.7	20.5	0.2875	105.0625
50	5.3	6	4.7	4.3	20.3	1.6475	103.0225
75	5.3	5.7	5.5	4.7	21.2	0.56	112.36
100	5.2	4.8	5	4.4	19.4	0.35	94.09
125	4.8	4.8	4.4	4.7	18.7	0.1075	87.4225
150	5.3	4.5	4.9	4.1	18.8	0.8	88.36
Total Pj	31	31.2	29.8	26.9	118.9	3.7525	590.3175
Pj^2 /k	160.1667	162.24	148.0067	120.6017	591.015

Anova Table
Source	df	SS	MSS	Var. Ratio	F-critic
B/w groups	5	1.2671	0.2534	2.1261	2.9013
Within Group	18	3.7525
i) B/w Subject	3	1.9646
ii) Error	15	1.7879	0.1192
Total:	23	5.0196

Since F - value 2.1261 < F critical value 2.9013, so we accept H0

Thus we conclude that there is no significant difference among the seeding rates.