21. Orange juice cans are filled using two methods. Two random samples one from each method produced the following results:

Method 1 : n1 = 40, ¯X1 = 21.78, S2 1 = 3.11 Method 2 : n2 = 40, ¯X2 = 20.71, S2 2 = 2.40

(a) Assuming normality, test at the 5% level of significance H0: σ2 1 = σ2 2 versus H1:

σ2 1 = σ2 2.

(b) Test, using the result of (a), the hypothesis H0: μ1 = μ2, versus H1: μ1 > μ2.