Test for Population Proportion

Statistics · Axiom Academy

LESSON Test for Population Proportion Learn how to test hypotheses about population proportions using z-tests 1. Setting Up Hypotheses for Proportions A hypothesis test for a population proportion always compares the population proportion p to a claimed value p 0 . The alternative hypothesis depends on what we're testing: Two-tailed: Testing if the proportion is different (H a : p ≠ p 0 ) Right-tailed: Testing if the proportion is greater (H a : p > p 0 ) Left-tailed: Testing if the proportion is less (H a : p 0 ) The test statistic measures how many standard errors the sample proportion is from the claimed value. We use the z-statistic : p̂ (p-hat) = sample proportion = x/n p 0 = claimed population proportion (from H 0 ) 3. Conditions for Valid Testing Before conducting a proportion test, we must verify two critical conditions to ensure the sampling distribution is approximately normal: At least 10 expected successes in the sample At least 10 expected failures in the sample The sampling distribution is approximately normal 4. Steps for Conducting a Proportion Test Follow this systematic approach to test a claim about a population proportion: Scenario: A candidate claims that 60% of voters support them. A pollster surveys 400 randomly selected voters and finds that 220 support the candidate. Test if the true proportion differs from 60% at α = 0.05. Hypotheses: H 0 : p = 0.60, H a : p ≠ 0.60 (two-tailed)

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