Record gunshot wounds in January and July from 50 emergency rooms to see if there is more gun violence in summer than winter. Which test is used to compare the two paired time periods?

Record gunshot wounds in January and July from 50 emergency rooms to see if there is more gun violence in summer than winter. Which test is used to compare the two paired time periods?

• A. Matched-Pairs T-Test
• B. Two-Sample T-Test
• C. One-Sample T-Test
• D. One-Proportion Z-Test

Answer: (A)

Two related measurements from the same emergency rooms across two seasons create paired data, so you focus on the difference within each pair (summer minus winter) and test whether that average difference is zero. This is exactly what the matched-pairs (paired) t-test does: it uses the differences for each ER to determine if there’s a systematic increase in gunshot wounds from winter to summer. The approach controls for differences between ERs by comparing each ER to itself, which is why it’s preferred over methods that assume independent samples. It relies on the differences being roughly normally distributed (with 50 pairs, you have enough data to rely on that approximation). In contrast, a two-sample t-test treats the two seasons as independent groups and ignores the pairing, a one-sample t-test compares a sample mean to a fixed value rather than a related pair of measurements, and a one-proportion z-test deals with proportions rather than means of counts.

Two related measurements from the same emergency rooms across two seasons create paired data, so you focus on the difference within each pair (summer minus winter) and test whether that average difference is zero. This is exactly what the matched-pairs (paired) t-test does: it uses the differences for each ER to determine if there’s a systematic increase in gunshot wounds from winter to summer. The approach controls for differences between ERs by comparing each ER to itself, which is why it’s preferred over methods that assume independent samples. It relies on the differences being roughly normally distributed (with 50 pairs, you have enough data to rely on that approximation). In contrast, a two-sample t-test treats the two seasons as independent groups and ignores the pairing, a one-sample t-test compares a sample mean to a fixed value rather than a related pair of measurements, and a one-proportion z-test deals with proportions rather than means of counts.