The following data shows the yield, in bushels per acre, categorized according t

Question

The following data shows the yield, in bushels per acre, categorized according to three varieties of corn and three different soil conditions. Assume that yields are not affected by an interaction between variety and soil conditions, and test the null hypothesis that variety has no effect on yield. Use a 0.05 significance level. Plot 1 Plot 2 Plot 3 Variety 1 156, 167, 162, 160, 145, 151 170, 162 169, 168 148, 155 Variety 2 172, 176, 179, 186, 161, 162 166, 179 160, 176 165, 170 Variety 3 175, 157, 178, 170, 169, 165, 179, 178 172, 174 170, 169

Explanation / Answer

For the given data in excel by using Anova: Two-Factor With Replication we get the out put as follows

Null Hypothesis (H0): The yields are not effeted by an interaction between variety and soil conditions

Alternative Hypothesis(H1): The yields are effeted by an interaction between variety and soil conditions

Conclusion: The P value > L.O.S

i.e 0.533402 > 0.05

Therefore we fail to reject the null hypothesis, so the yields are not effeted by an interaction between variety and soil conditions

Anova: Two-Factor With Replication SUMMARY plot 1 plot 2 plot 3 Total variety 1 Count 4 4 4 12 Sum 655 659 599 1913 Average 163.75 164.75 149.75 159.4167 Variance 37.58333 19.58333 18.25 71.7197 variety 2 Count 4 4 4 12 Sum 693 701 658 2052 Average 173.25 175.25 164.5 171 Variance 31.58333 120.9167 16.33333 69.81818 variety 3 Count 4 4 4 12 Sum 689 694 673 2056 Average 172.25 173.5 168.25 171.3333 Variance 106.25 11.66667 4.916667 38.9697 Total Count 12 12 12 Sum 2037 2054 1930 Average 169.75 171.1667 160.8333 Variance 67.65909 64.51515 80.33333 ANOVA Source of Variation SS df MS F P-value F crit plots 1105.167 2 552.5833 13.54801 8.43E-05 3.354131 varieties 753.1667 2 376.5833 9.232917 0.00088 3.354131 Interaction 131.1667 4 32.79167 0.803973 0.533402 2.727765 Within 1101.25 27 40.78704 Total 3090.75 35

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