107 parts made from alloy 1 and 48 parts made from alloy 2 were subjected to str

Question

107 parts made from alloy 1 and 48 parts made from alloy 2 were subjected to stress tests. 17 parts from alloy 1 and 15 parts from 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 aloy 2 at a-0.01? Assume independent samples. Question 1 For the hypothesis stated above (in terms of alloy1- alloy2) Part A What is the decision rule?in only one of the following statements. If the hypothesis is one tailed: Reject Ho if If the hypothesis is two tailed Reject Ho if or Part BWhat is the test statistic? Question 2 Find the 95% confidence interval (in terms of alloy2-alloy 1). Left Endpoint- Right Endpoint-

Explanation / Answer

we reject h0 if the p value is less than the alpha of 0.05

as we are interested in atleast as large as the proportion of non passing parts from alloy2 , hence it becomes a right tail test , which is a 1 tail test

we know that the test stat is given as

z = (p1-p2)/sqrt(p1*(1-p1)/n1 + p2*(1-p2)/n2 )

here n1 = 107 , p1 = 17/107= 0.158 and n2 = 48 and p2= 15/48 = 0.312

z = (0.158- 0.312)/sqrt(0.158*(1-0.158)/107 + 0.312*(1-0.312)/48 )

= -2.037

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