Q#1 (i) An agronomist planted three comparable test plots each with four varieti
ID: 3020370 • Letter: Q
Question
Q#1 (i) An agronomist planted three comparable test plots each with four varieties of wheat and obtained the following yields (in pounds per plot):
Variety A: 57, 62, 61
Variety B: 52, 53, 60
Variety C: 53, 56, 56
Variety D: 56, 59, 59
(a) Compute between- sample variance -------------------------.
(b) Compute within- sample variance ----------------------------.
(c) Use ANOVA to test at the 0.05 level of significance whether the differences among the four sample means can be attributed to variety or chance (give full ANOVA table values).
Explanation / Answer
An agronomist planted three comparable test plots each with four varieties of wheat and obtained the following yields (in pounds per plot)
The hypothesis for the test is,
H0 : mu1 = mu2 = mu3 = mu4 Vs H1 : Atleast one of the mu is not equal.
where, mu1, mu2, mu3 and mu4 are population means of four varieties.
We can done ANOVA by using EXCEL.
steps :
between sample variance = 12.8333
within sample variance = 6.25
level of significance (alpha) = 0.05
From the output,
F = 2.0533
critical value = 6.5914
F < critical value
Accept H0 at 5% level of significance.
Conclusion : All the four means are equal.
Anova: Single Factor SUMMARY Groups Count Sum Average Variance 57 2 123 61.5 0.5 52 2 113 56.5 24.5 53 2 112 56 0 56 2 118 59 0 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 38.5 3 12.83333 2.053333 0.249107 6.591382 Within Groups 25 4 6.25 Total 63.5 7Related Questions
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