A farmer would like to know if a new fertilizer increases crop yield. The farmer records the yield for 10 different fields prior to adding fertilizer and after adding the fertilizer. Which test works?

A farmer would like to know if a new fertilizer increases crop yield. The farmer records the yield for 10 different fields prior to adding fertilizer and after adding the fertilizer. Which test works?

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

Answer: (A)

This question tests using a paired (matched) design to compare two related measurements on the same subjects. Since the farmer measured yield on the same fields before and after applying fertilizer, the data are linked within each field. The appropriate test is a paired samples t-test, which analyzes the mean change in yield. How it works: for each field, compute the difference in yield after minus before. Then look at the average of these differences and how much they vary. The test statistic is t = (mean difference) / (standard deviation of differences / sqrt(n)), with n being the number of fields. If this t is large in magnitude, it suggests fertilizer affects yield. The degrees of freedom are n − 1 (here, 9). This approach is better than a two-sample t-test because the two measurements come from the same fields and are not independent; the paired test accounts for that linkage and focuses on the effect of the fertilizer on the yield within each field. If the differences aren’t roughly normal, a nonparametric alternative like the Wilcoxon signed-rank test can be considered.

This question tests using a paired (matched) design to compare two related measurements on the same subjects. Since the farmer measured yield on the same fields before and after applying fertilizer, the data are linked within each field. The appropriate test is a paired samples t-test, which analyzes the mean change in yield.

How it works: for each field, compute the difference in yield after minus before. Then look at the average of these differences and how much they vary. The test statistic is t = (mean difference) / (standard deviation of differences / sqrt(n)), with n being the number of fields. If this t is large in magnitude, it suggests fertilizer affects yield. The degrees of freedom are n − 1 (here, 9).

This approach is better than a two-sample t-test because the two measurements come from the same fields and are not independent; the paired test accounts for that linkage and focuses on the effect of the fertilizer on the yield within each field. If the differences aren’t roughly normal, a nonparametric alternative like the Wilcoxon signed-rank test can be considered.