Proportion Test Examples

Statistics · Axiom Academy

EXAMPLE Proportion Test Examples Master hypothesis testing for population proportions through worked examples Problem: Voter Support Analysis Scenario: A political analyst claims that a candidate has majority support (more than 50%). In a random sample of 400 likely voters, 224 support the candidate. Question: Does this provide significant evidence at the level that the candidate has majority support? Excellent work! You've completed three comprehensive proportion test examples. Here's what we learned: Hypothesis Setup: For proportion tests, uses the claimed value, and reflects what we're testing (greater than, less than, or not equal to). Conditions Matter: Always verify the success-failure condition: and must both be at least 10 for the normal approximation to be valid. Test Statistic Formula: The z-statistic measures how many standard errors the sample proportion is from the hypothesized value: . P-value Interpretation: The p-value tells us the probability of observing our sample result (or more extreme) if the null hypothesis is true. Smaller p-values provide stronger evidence against . One-tailed vs Two-tailed: Use one-tailed tests when testing if a proportion is greater than or less than a value; use two-tailed when testing if it differs (in either direction). Context is Critical: Always state your conclusion in the context of the problem, explaining what the statistical result means for the real-world question.

This is the written version of the interactive lesson above. See the full Statistics course.