Practice Two-Sample Tests in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Hypothesis tests and confidence intervals for comparing parameters (means or proportions) of two independent populations. The two-sample t-test compares means; the two-proportion z-test compares proportions.
You have two separate groups—say, students taught with Method A vs Method B—and want to know if there's a real difference. Unlike paired tests where the same subjects appear in both groups, here the groups are completely independent. You compare the two sample statistics and ask: 'Is the gap between these groups larger than what random variation alone would produce?'
Example 1
mediumTest whether two teaching methods differ in effectiveness. Method A (n_A=30, \bar{x}_A=75, s_A=8) vs. Method B (n_B=30, \bar{x}_B=80, s_B=10). Use a two-sample z-test at \alpha=0.05.
Example 2
hardConstruct a 95% confidence interval for \mu_A - \mu_B given: \bar{x}_A=50, \bar{x}_B=45, s_A=6, s_B=8, n_A=n_B=25.
Example 3
easyWhen should a two-sample t-test be used instead of a z-test, and what is the key assumption about the two groups?
Example 4
hardTwo independent samples: Group 1 (n=20, \bar{x}=100, s=15), Group 2 (n=20, \bar{x}=95, s=20). Calculate the t-statistic and df for a Welch's t-test (unequal variances).