3)

3. (16 pts.) A new diet has been developed for raising beef cows. Two random samples of size fteen are independently selected, and one is given the new diet and the other is given the stande diet. After 13 weeks, the weight gain was measured, and it was found that f) = 35 with s; = 3 and f2 = 29 with s; = 6. Let Jul, and #2 represent the mean weight gain 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. (a) Test the following hypotheses using a=0.l : Hg: in; =#2= Ha: a; e #2 (b) Calculate 99% condence interval for pi p2