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One proportion Two proportions (from independent samples or a randomized experiment) One sample t (including Matched Pairs) Two sample t (from independent samples or a randomized experiment) Population(s) p p1 , p 2 1 , 2 Mean of the sampling distribution p p1 p2 1 2 Sample(s) p̂ pˆ 1 , pˆ 2 x x1 , x2 Standard Deviation of the sampling dist’n of the statistic Estimate, called the Standard Error SE pˆ (1 pˆ ) n Check for SRS design of study Check for Large-sample: normality for a successes 15 Confidence failures 15 Interval Plus-four: See list. Check for normality for a Significance Test Critical Value npo 10 n(1 po ) 10 See conditions list. z* depends only on confidence level p1 (1 p1 ) p2 (1 p2 ) n1 n2 p(1 p) n SE n pˆ 1 (1 pˆ 1 ) pˆ 2 (1 pˆ 2 ) n1 n2 Two independent SRSs or random assignment to groups. Large-sample: In each sample successes 10 failures 10 12 SE n1 s n 2 SE 22 n2 2 s1 s 2 n1 n2 SRS Two independent SRSs or random assignment to groups. See conditions list. Same conditions for confidence interval and significance test. See conditions list. Same conditions for confidence interval and significance test. See conditions list. Same conditions for confidence interval and significance test. See conditions list. Same conditions for confidence interval and significance test. t* depends on confidence level and degrees of freedom t* depends on confidence level and degrees of freedom Plus-four: See conditions list. In each sample: successes 5 failures 5 See conditions list. z* depends only on confidence level One proportion Margin of Error Confidence Interval E z * pˆ (1 pˆ ) n pˆ (1 pˆ ) pˆ z * n z Two proportions (from independent samples or a randomized experiment) z * pˆ1 (1 pˆ1 ) pˆ 2 (1 pˆ 2 ) n1 n2 pˆ (1 pˆ1 ) pˆ 2 (1 pˆ 2 ) ( pˆ1 pˆ 2 ) z * 1 n1 n2 pˆ po One sample t (including Matched Pairs) t * s x t * n t z ( pˆ1 pˆ 2 ) 0 pˆ (1 pˆ ) pˆ (1 pˆ ) n1 n2 Where we use the pooled proportion pˆ total successes n1 n2 We use Normal table to find an exact P-value or t-table to find an interval containing the P-value s12 s2 2 n1 n2 ( x1 x2 ) t * s12 s2 2 n1 n2 HO : 1 2 HO : p1 p2 then t * If If po (1 po ) n Where po is the Test statistic hypothesized population proportion; We use Normal Table to find an exact P-value or t-table to find an interval containing the P-value s n Two sample t (from independent samples or a randomized experiment) x o s n Where o is the hypothesized population mean ; we use t-table to find an interval containing the P-value then t ( x1 x2 ) 0 s12 s2 2 n1 n2 Software gives us the exact degrees of freedom and Pvalue. By hand, use the smaller sample size minus 1 and an interval containing the P-value.