Question

9.3-2. Let ; be the average yield in bushels per acre of variety i of corn, i = 1,2,3,4. In order to test the hypoth- esis Ho: M1 = M2 = 3 = 44 at the 5% significance level, four test plots for each of the four varieties of corn are planted. Determine whether we accept or reject Ho if the yield in bushels per acre of the four varieties of corn are, respectively, as follows: X: X2: X3: X4: 158.82 176.84 180.16 151.58 166.99 165.69 168.84 163.51 164.30 167.87 170.65 164.57 168.73 166.18 173.58 160.75

Answer 1

Answer:

Hypothesis:

Null Hypothesis h0: U1 = U2 =U3=U4

alternative hypothesis Ha: at one Ui is different

and alph = 0.05

ANOVA by minitab

ANOVA: X1, X2, X3, X4.

Source DF SS MS F P

Factor 2 388.3 129.4 4.91 0.019

Eroor 12 316.5 26.4

Total 15 704.7

S = 5.135, R-sq = 55.1% R-sq(ad) = 43.87%

from the table

SSTo = 704.7

SSTr = 388.3

SSE = 316.5

dfTo = 15

dfTr = 2

dfE = 12

p = 0.019 (<alpha)

Hence reject Null Hypothesis.