Two-Sample Tests Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
When should a two-sample t-test be used instead of a z-test, and what is the key assumption about the two groups?

Solution

  1. 1
    Use t-test when: population standard deviation ฯƒ\sigma is unknown (use sample SD instead); typically when n<30n < 30 or when normality is assumed
  2. 2
    Use z-test when: ฯƒ\sigma is known; or nn is large enough for CLT (nโ‰ฅ30 per group)
  3. 3
    Key assumption: the two groups must be INDEPENDENT โ€” no pairing or matching; units in one group are unrelated to units in the other group

Answer

Use t-test when ฯƒ is unknown (small n). Key assumption: the two groups are independent.
The t-distribution accounts for uncertainty in estimating ฯƒ from sample data. As n increases, the t-distribution approaches the z-distribution. The independence assumption distinguishes two-sample tests from paired tests.

About Two-Sample Tests

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.

Learn more about Two-Sample Tests โ†’

More Two-Sample Tests Examples

Example 1 medium

Test whether two teaching methods differ in effectiveness. Method A ([formula], [formula], [formula]

Example 2 hard

Construct a 95% confidence interval for [formula] given: [formula], [formula], [formula], [formula],

Example 4 hard

Two independent samples: Group 1 ([formula]), Group 2 ([formula]). Calculate the t-statistic and df

โ† All Two-Sample Tests Examples Two-Sample Tests Concept