Three different pesticides can be used to control pest infestation of grapes. It is suspected that pesticide 3 is more effective than the other two. In a particular vineyard, three different plantings of pinot noir grapes are selected for study. The following results on yield are obtained:

If μ_i is the true mean yield after treatment with the ith pesticide, you are interested in the quantity μ = ½(μ₁ + μ₂) €“ μ₃ which measures the difference in mean yields for pesticides 1 and 2 and pesticide 3. If the sample sizes ni are large, the estimator (say, μ) obtained by replacing each individual μ_i by Xi is approximately normal.

(a) Find an approximate 100(1 ˆ’ x)% large-sample confidence interval for μ.

(b) Do these data support the claim that pesticide 3 is more effective than the other two? Use α = 0.05 in determining your answer.

Transcribed Image Text:

X; (bushels/ plant) n, (number of plants) Pesticide 1 4.6 0.7 100 2 3 5.2 0.6 120 130 6.1 0.8