Question

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

Which of the following are the correct null hypotheses? μ₁ is the average yield in bushels per acre for the control.

H₀: μ₁ − μ_j ≠ 0 where j ≠ 1
H₀: μ₁ − μ_j=0 where j ≠ 1
H_a: μ₁ − μ_j < 0 where j ≠ 1
H₀: μ₁ − μ_j=0 where j = 2

Which of the following are the correct alternative hypotheses? μ₁ is the average yield in bushels per acre for the control.

H₀: μ₁ − μ_j < 0 where j ≠ 1
H_a: μ₁ − μ_j > 0 where j ≠ 1
H_a: μ₁ − μ_j ≠ 0 where j ≠ 1
H_a: μ₁ − μ_j < 0 where j ≠ 1

How many pairwise comparisons is the farmer making?

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

Answer 1