Question

A farmer is interested in comparing three different brands of fertilizer, Grow'em Big, Jim's Fertilizer and...

A farmer is interested in comparing three different brands of fertilizer, Grow'em Big, Jim's Fertilizer and Sally's Best. He planted wheat in 4 different fields, one with each brand of fertilizer and the fourth one with no fertilizer as a control. Each field is 69 acres in size. The farmer recorded the yield in bushels for each acre of every field. They are interested in knowing whether certain brands of fertilizer have an impact on yield. Assume that the mean of the control is μ1, Grow'em Big is μ2, Sally's Best is μ3 and Jim's Fertilizer is μ4. The summary statistics for the farmer's experiment are as follows:

 Control Grow'em Big Jim's Fertilizer Sally's Best Mean 22.01 25.35 45.41 23.50 Sum of Squares: 33951.24 78820.37 221676.00 260258.25

How many pairwise comparisons is the farmer making?

Assuming a confidence level of 95 %, what would be the value of α*

(I tried 0.05 its incorrect)

For μ1−μ4 (control vs. Jim's Fertlizer) do we reject the null hypothesis? For μ1−μ3 (control vs. Sally's Best), do we reject the null hypothesis? And for μ1−μ2 (control vs. Grow'em Big), do we reject the null hypothesis?

pairwise comparisons = 3

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α* = 0.05/3 = 0.0167

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no. of treatments,k=   4
DF error =N-k=   272
MSE=   2186.4186
t-critical value,t(α/2,df)=   2.4089

 confidence interval mean difference critical value lower limit upper limit µ1-µ2 -3.34 19.18 -22.5166 15.8366 µ1-µ3 -1.49 19.18 -20.6666 17.6866 µ1-µ4 -23.40 19.18 -42.5766 -4.2234

if confidence interval do not contains zero, then means are significantly different.

For μ1−μ4 (control vs. Jim's Fertlizer) do we reject the null hypothesis?

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For μ1−μ3 (control vs. Sally's Best), do we reject the null hypothesis?

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And for μ1−μ2 (control vs. Grow'em Big), do we reject the null hypothesis?

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