Two alloys A and B are being used to manufacture a certain steel product. An exp
ID: 3177622 • Letter: T
Question
Two alloys A and B are being used to manufacture a certain steel product. An experiment needs to be designed to compare the two in terms of maximum load capacity in tons. This is the maximum that can be tolerated without breaking. It is known that the two standard deviations in load capacity are equal at 5 tons each. An experiment is conducted in which 30 specimens of each alloy (A and B) are tested and the results gave x_a = 49.5 x_b = 45.5 x_a - x_b = 4 the manufacturer of Alloy A are convinced that this evidence shows conclusively that mu_A > mu_B and strongly supports their alloy. Manufacturer of alloy B claim that the experiment could easily have given x_a - x_b = 4 even if the two population means are equal. in other words, "things are inconclusive!". Make an argument that manufacturers of Alloy B are wrong. Do it by computing P(X_a - X_b > 4|mu_A = mu_b) Do you think this data strongly support alloy A?Explanation / Answer
(a) xA-bar = 49.5 ; xB-bar = 45.5
= 5 => = 5
so lets do null hypothesis H0 : A = B
alternative hypothesis H1 : A - B >= 0
so P( XA-bar - XB- bar >4 if A = B ) will be calculated by Z value = (XA-bar - XB- bar)/sqrt[(s12/n1 + s22/n2]
= 4/ sqrt(2 * 25/30) =3.099
for this Z value in Z - table P value is = 1- 0.9990 = 0.001
so we can say that this is very low probability and we can say that manufactures of alloy B is wrong. As it is not under even 0.005 significance level.
(b) Yes this data very very strongly support alloy A.