The following data are average yields in busheis per acre on four plots of land

ID: 3178688 • Letter: T

Question

The following data are average yields in busheis per acre on four plots of land for four different varieties of corn. Yield (busheis per acre) is the response variable and corn variety is the treatment factor with four levels. Use the data below and corresponding results of section 8.2 task 1 for Questions on this task. For a = 0.05, calculate Tukey's W. Using Tukey's W, calculate a 95 % confidence interval for each of the six pairwise comparisons mu_i - mu_j. Use Tukey's W or the confidence intervals to determine all pairwise comparisons were Ho: mu_i - mu_j = 0 is rejected.

Explanation / Answer

c = 4 and (n – c) = (16 – 4) = 12 degrees of freedom: Qa= 4.20.

Critical Range= Qa*MSW/2(1/nj+1/nj’)

= 4.20*24.84/2(1/4+1/4)

= 4.20*2.49

= 10.4663

= 10.47

X1-X2=74.21-77.4=-3.19

X1-X3=74.21-83.06=-8.85

X1-X4=74.21-69.35=4.86

X2-X3=77.4-83.06=-5.66

X2-X4=77.4-69.35=8.05

X3-X4= 83.06-69.35=13.71

All except X3-X4 are smaller than critical range and hence only at X3-X4, there is a significant difference at 5% level of significance.

Corn Variety 1 2 3 4 68.82 84.84 90.16 61.58 76.99 75.69 77.84 70.51 74.3 72.87 80.65 74.57 76.73 76.18 83.58 70.75 Mean 74.21 77.4 83.06 69.35 SUMMARY Groups Count Sum Average Variance 1 4 296.84 74.21 14.37966667 3.792053094 2 4 309.58 77.395 26.7623 5.173229166 3 4 332.23 83.0575 27.91229167 5.283208463 4 4 277.41 69.3525 30.30895833 5.505357239 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 396.590525 3 132.1968417 5.321761759 0.014544134 3.490294819 Within Groups 298.08965 12 24.84080417 Total 694.680175 15