A New Diet Has Been Developed for Raising Beef Cows

Multiple Choice

A new diet has been developed for raising beef cows. Two random samples of size 9 are independently selected, and one is given the standard diet while the other is given the new diet. After 18 weeks, the weight gain was measured for each cow. It was found that x̄₁= 30 with S₁= 8 and x̄₂= 26 with S₂= 6. Let μ₁ and μ₂ represent the mean weight gains we would observe for the entire population of beef cows when on, respectively, a new diet and a standard diet. Assume that two-sample t procedures are safe to use. Suppose the researcher had wished to test the following hypotheses:
H₀: μ₁ = μ₂ versus H_a: μ₁ > μ₂
What is the numerical value of the two-sample t statistic for this test?

A) 0.36
B) 1.20
C) 2.57
D) 4.00