Question 1137984: 110 parts made from alloy 1 ad 50 parts made from alloy 2 were subjected to stress tests. 16 parts of alloy 1 and 13 parts of alloy 2 did not pass the test. Can we reject the hypothesis that the proportion of nonpassing parts from alloy 1 is at least as large as the proportion of nonpassing parts from alloy 2 at a=0.01? Assume independent samples.
q1. for the hyphotesis test stated above in terms of alloy 1-alloy 2
what is the decision rule? if the hypothesis is one tailed
reject Ho if z stat < ___________
what is the test statistic? ____________
a2. Find the 80% confidence interval in terms of alloy 2- alloy 1
left endpoint: _________ right endpoint:______________
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho=two proportions are equal
Ha=they aren't equal
alpha is 0.01 P{reject Ho|Ho true}
z= difference in means/SE ; SE is sqrt ((p1*(1-p1)/n1) + p2(1-p2)/n2))
reject z if |z|>1.96
phat 1=0.145 16/110
phat 2=0.26 or 13/50
NOTE: this is done with alloy1-alloy2. Change all the signs at the end.
SE is sqrt [(0.145*0.855)/110+(.26*.74)/50]=0.00497, so SE=0.070. The difference is -0.115, and the z-value is -1.64
80%CI has a z=+/-1.28
so the half-interval is 1.28*0.07=0.0896
The difference between the two is -0.115+/-0.089 or (-0.204, -0.026) meaning 0, or equality is not in the 80% CI, which is another way of saying they are from different populations.
alloy2-alloy1 CI is (0.026, 0.204)
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