A factory installed scrubbers; measurements of sulfate levels before and after installation were taken, but not paired. Which test compares the two independent samples?

A factory installed scrubbers; measurements of sulfate levels before and after installation were taken, but not paired. Which test compares the two independent samples?

• A. Paired t-test
• B. 1-sample t-test
• C. ANOVA
• D. 2-sample t-test

Answer: (D)

When you’re comparing the means of two groups that don’t influence each other, you use a two-sample t-test. In this scenario, the sulfate measurements before installation and after installation come from separate, independent sets of observations, not paired measurements from the same units. The two-sample t-test assesses whether the average sulfate level differs between these two independent groups, which is exactly the question here about the effect of the scrubbers. If the data had been paired—each unit measured before and after—the paired t-test would be more appropriate because it analyzes the differences within each unit, increasing power. A 1-sample t-test would compare a single group to a known reference value, not two groups. ANOVA would be used for comparing means across three or more groups (though it can handle two groups, the two-sample t-test is the direct, standard choice for two independent samples).

When you’re comparing the means of two groups that don’t influence each other, you use a two-sample t-test. In this scenario, the sulfate measurements before installation and after installation come from separate, independent sets of observations, not paired measurements from the same units. The two-sample t-test assesses whether the average sulfate level differs between these two independent groups, which is exactly the question here about the effect of the scrubbers.

If the data had been paired—each unit measured before and after—the paired t-test would be more appropriate because it analyzes the differences within each unit, increasing power. A 1-sample t-test would compare a single group to a known reference value, not two groups. ANOVA would be used for comparing means across three or more groups (though it can handle two groups, the two-sample t-test is the direct, standard choice for two independent samples).