Question

Let u_i be the average yield in bushels per acre of variety i of corn, i=1,2,3,4.In order to test the hypothesis H₀ :u₁=u₂=u₃=u₄ at the 5% significance level, four test plots for each of the four varieties of corn are planted. Determine whether we reject or accept the null hypothesis if the yield in bushels per acre of the four varieties are as follows:

x₁: 158.82, 166.99, 164.30, 168.73

x₂: 176.84, 165.69, 167.87, 166.18

x₃: 180.16, 168.84, 170.65, 173.58

x₄: 151.58, 163.51, 164.57, 160.75

Answer 1

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	4	658.84	164.71	18.73967
Column 2	4	676.58	169.145	27.18897
Column 3	4	693.23	173.3075	24.68396
Column 4	4	640.41	160.1025	34.87396
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	388.2805	3	129.4268	4.907805	0.018838	3.490295
Within Groups	316.4597	12	26.37164
Total	704.7402	15