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Hypothesis Testing: Two Population Means and Two Population Proportions: Summary of Types of Hypothesis Tests

Module by: Dr. Barbara Illowsky, Susan Dean

Rule 1: Two Population Means

  1. Populations are independent and population standard deviations are unknown.
  2. Populations are independent and population standard deviations are known (not likely).

Rule 2: Matched or Paired Samples

Rule 3: Two Population Proportions

  1. Populations are independent.

DECISION AND CONCLUSION

The following hypotheses tests for two independent population means have the same decision and conclusion.

  • H o : μ 1 ≥ μ 2 H a : μ 1 < μ 2 H o : μ 1 ≥ μ 2 H a : μ 1 < μ 2
  • H o : μ 2 ≤ μ 1 H a : μ 2 > μ 1 H o : μ 2 ≤ μ 1 H a : μ 2 > μ 1
The following hypotheses tests for two population proportions have the same decision and conclusion.
  • H o : p 1 ≥ p 2 H a : p 1 < p 2 H o : p 1 ≥ p 2 H a : p 1 < p 2
  • H o : p 2 ≤ p 1 H a : p 2 > p 1 H o : p 2 ≤ p 1 H a : p 2 > p 1

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