Two independent samples of exam scores from two different schools are compared to see if their means differ. Which test?

Two independent samples of exam scores from two different schools are compared to see if their means differ. Which test?

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

Answer: (C)

When you want to know whether two independent groups differ in their average value, you use a two-sample test for means. The two-sample t-test compares the difference between the two sample means to what would be expected if the true population means were the same, taking into account the variability in each sample. It’s appropriate here because the scores are continuous, the samples come from two different schools (independent), and the population standard deviations are typically unknown. If you assume equal variances, you can use the pooled version; if you don’t want to assume equal variances, you’d use the Welch version. The other options don’t fit: a one-sample t-test compares a single sample mean to a known value, and z-tests for means or proportions are used under known population variance or for proportions, respectively.

When you want to know whether two independent groups differ in their average value, you use a two-sample test for means. The two-sample t-test compares the difference between the two sample means to what would be expected if the true population means were the same, taking into account the variability in each sample. It’s appropriate here because the scores are continuous, the samples come from two different schools (independent), and the population standard deviations are typically unknown.

If you assume equal variances, you can use the pooled version; if you don’t want to assume equal variances, you’d use the Welch version. The other options don’t fit: a one-sample t-test compares a single sample mean to a known value, and z-tests for means or proportions are used under known population variance or for proportions, respectively.