Find the p–value for this test. What will your decision be if α = .01? What if α = .05?

Question

 A researcher finds that swine in their study gain an average of 8  pounds or more after being fed the trial feed. The feed company sponsor wanted to check this claim and took a random sample of 32 pigs and found that they gained an average of 8.6  pounds within the first month of the trial with a standard deviation of 2.2 pounds. Find the p–value for this test. What will your decision be if α = .01? What if α = .05?

Answer 1

From the word problem form the hypothesis test:

H₀: µ₀ ≥ 8 pounds gained : This is the CLAIM, and is a left tail test

H_a: µ₀ < 8 pounds gained

use the t-distribution for df=32 (n-1) because the problem gives the sample standard deviation, not the population σ

you will calculate a t value of 1.453 and a p-value of .9335

p > α for both α = .01 and .05; do NOT reject H_o

There is sufficient evidence to support the researcher's claim that the average weight gain is more than 8 points