23. Two randomly selected groups of 70 trainees each are taught a new assembly line operation by two different methods, with the following results when the groups are tested:

Group 1 : n1 = 70, ¯X1 = 268.8, S1 = 20.2 Group 2 : n2 = 70, ¯X2 = 255.4, S2 = 26.8

(a) Assuming normality, test the hypothesis σ1 = σ2 versus σ2 > σ1. Use α = 0.01.

(b) Using the result of (a), test at the 5% level of significance the hypothesis H0: μ1 =

μ2 versus H1: μ1 > μ2.

24. The following data give the results for iron content of ore using two methods A (dichromate)

or B (thioglycolate) on 10 different samples of ore.

Sample number Percent iron by method A Percent iron by method B 1 28.22 28.27 2 33.95 33.99 3 38.25 38.20 4 42.52 42.42 5 37.62 37.64 6 37.84 37.85 7 36.12 36.21 8 35.11 35.20 9 34.45 34.40 10 52.83 52.86 Assuming normality, use the method of paired comparisons to test whether these two methods yield significantly different percentages of iron at the 5% level of significance.