Stainless steels are susceptible to stress corrosion cracking under certain cond

Question

Stainless steels are susceptible to stress corrosion cracking under certain conditions. An engineer wants to determine the proportion of steel alloy failures that are due to stress corrosion cracking.

a) In the absence of preliminary data, how large a sample must be taken so as to be sure that a 99% confidence interval will specify the proportion to within +/- 0.05?

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

c) Based on the data in part (b), estimate the sample size needed so that the 98% confidence interval will specify the proportion to be within +/- 0.05

Explanation / Answer

Stainless steels are susceptible to stress corrosion cracking under certain conditions. An engineer wants to determine the proportion of steel alloy failures that are due to stress corrosion cracking. a) In the absence of preliminary data, how large a sample must be taken so as to be sure that a 99% confidence interval will specify the proportion to within +/- 0.05? b) In a sample of 200 failures, 30 were caused by stress corrosion cracking. Find a 98% confidence interval for the proportion of failures caused by stress corrosion cracking. c) Based on the data in part (b), estimate the sample size needed so that the 98% confidence interval will specify the proportion to be within +/- 0.05

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