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Question : The quality department at an electronics company


The quality department at an electronics company has noted that, historically, 92% of the units of a specific product pass a test operation, 6% fail the test but are able to be repaired, and 2% fail the test and need to be scrapped. Due to recent process improvements, the quality department would like to test if the rates have changed. A recent sample of 500 parts revealed that 475 parts passed the test, 18 parts failed the test but were repairable, and 7 parts failed the test and were scrapped.
a. State the null and alternative hypotheses to test if the current proportions are different than the historical proportions.
b. Calculate the value of the test statistic and the p-value.
c. At the 5% significance level, what is your conclusion? Would your conclusion change at the 1% significance level?