Two suppliers' shipments are tested for defect rates. The contract accepts the shipment with the smallest rate. Do the defect rates vary between suppliers?

Two suppliers' shipments are tested for defect rates. The contract accepts the shipment with the smallest rate. Do the defect rates vary between suppliers?

• A. 1-proportion z-test
• B. 2-sample t-test
• C. 2-proportion z-test
• D. Matched pairs t-test

Answer: (C)

The main idea is comparing two proportions. Each supplier has a defect rate, which is a proportion of items defective in their shipments. To test whether these rates differ, you use a two-proportion z-test. This test looks at the observed defect proportions from each supplier (p1 and p2) and asks if the difference between them is large enough to conclude a real difference in defect rates, rather than just random variation. Under the null hypothesis that the true defect rates are the same, you combine the data to get a pooled proportion and compute a z statistic to see how extreme the observed difference is under a standard normal distribution. If the sample sizes are large enough (np and n(1−p) reasonably large for both suppliers), this approximation is appropriate. Why the other options don’t fit: a one-proportion z-test compares a single proportion to a fixed value, not two groups. a two-sample t-test compares means, not proportions. a matched pairs t-test is for paired measurements on the same subjects (before/after or matched pairs), not independent samples from two different suppliers.

The main idea is comparing two proportions. Each supplier has a defect rate, which is a proportion of items defective in their shipments. To test whether these rates differ, you use a two-proportion z-test. This test looks at the observed defect proportions from each supplier (p1 and p2) and asks if the difference between them is large enough to conclude a real difference in defect rates, rather than just random variation. Under the null hypothesis that the true defect rates are the same, you combine the data to get a pooled proportion and compute a z statistic to see how extreme the observed difference is under a standard normal distribution. If the sample sizes are large enough (np and n(1−p) reasonably large for both suppliers), this approximation is appropriate.

Why the other options don’t fit: a one-proportion z-test compares a single proportion to a fixed value, not two groups. a two-sample t-test compares means, not proportions. a matched pairs t-test is for paired measurements on the same subjects (before/after or matched pairs), not independent samples from two different suppliers.