Inference Formulas & Conditions Test Conditions Null Hypothesis Test Statistic Confidence Interval One-Sample z-test (for 1.) Z Test Z Interval a population mean) 2.) SRS 3.) population is normal, or Ho: µ = µo large sample size (n 30) ≥ 4.) Two-Sample z-test (for 1.) are known 2 Sample Z Test 2 Sample Z Interval a difference in 2 2.) SRS population means) 3.) population is normal, or Ho: µ1 = µ2 large sample size ( 30) ≥ 4.) Samples are Independent T Test One-Sample t-test 1.) SRS T Interval (for a population mean) 2.) population is normal, or Ho: µ = µo sample size (n 30) ≥ with 1 df n – 3.) (for 1.) SRS 2 Sample T Test 2 Sample T Interval Two-Sample t-test a difference in 2 2.) population is normal, or or population means) large sample size ( 30) With smaller of or df ≥ 3.) Samples are independent df from calculator Matched Pairs t-test 1.) samples are not independent T Test T Interval (they are matched) 2.) SRS with 1 df n – 3.) differences are normal or large sample size (n 30) ≥
Inference Formulas & Conditions Test Conditions Null Hypothesis Test Statistic Confidence Interval One-Sample z-test (for a population mean) 1.) 2.) SRS 3.) population is normal, or large sample size (n ≥ 30) 4.) Ho: µ = µo Z Test Z Interval Two-Sample z-test (for a difference in 2 population means) 1.) are known 2.) SRS 3.) population is normal, or large sample size ( ≥ 30) 4.) Samples are Independent Ho: µ1 = µ2 2 Sample Z Test 2 Sample Z Interval One-Sample t-test (for a population mean) 1.) SRS 2.) population is normal, or sample size (n ≥ 30) 3.) Ho: µ = µo T Test with n – 1 df T Interval Two-Sample t-test (for a difference in 2 population means) 1.) SRS 2.) population is normal, or large sample size ( ≥ 30) 3.) Samples are independent or 2 Sample T Test With smaller of or df df from calculator 2 Sample T Interval Matched Pairs t-test 1.) samples are not independent (they are matched) 2.) SRS 3.) differences are normal or large sample size (n ≥ 30) T Test with n – 1 df T Interval
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