Stainless steel can be susceptible to stress corrosion crack

Stainless steel can be susceptible to stress corrosion cracking under certain conditions. A materials engineers is interested in determining the proportion of steel alloy failures that are due to stress corrosion cracking.

B. In a sample of 200 failures, 30 of them were caused by stress corrosion cracking. Find a 98% confidence interval for the proportion of failures caused by stress cirrisuib cracking.

Solution

(a) We use p=0.5 as estimated.

Given a=1-0.98=0.02, Z(0.01) = 2.33 (from standard normal table)

So n=(Z/E)^2*p*(1-p)

=(2.33/0.05)^2*0.5*0.5

=542.89

Take n=543

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(b) p=30/200 = 0.15

So the lower bound is

p - Z*sqrt(p*(1-p)/n) =0.15 -2.33*sqrt(0.15*(1-0.15)/200) =0.09117038

So the upper bound is

p + Z*sqrt(p*(1-p)/n) =0.15 +2.33*sqrt(0.15*(1-0.15)/200) =0.2088296