ATTACHMENT (ALL VERSIONS) – 41 – STATS 101 STATS 101G STATS 108 FORMULAE Confidence intervals and t-tests Confidence interval: estimate± t×se(estimate) t-test statistic: t0 = estimate− hypothesised value standard error Applications: 1. Single mean μ: estimate = x; df = n− 1 2. Single proportion p: estimate = p̂; df = ∞ 3. Difference between two means μ1 − μ2: (independent samples) estimate = x1 − x2; df = min(n1 − 1, n2 − 1) 4. Difference between two proportions p1 − p2: estimate = p̂1 − p̂2; df = ∞ Situation (a): Proportions from two independent samples Situation (b): One sample of size n, several response categories Situation (c): One sample of size n, many yes/no items The F -test (ANOVA) F -test statistic: f0 = s2B s2W ; df1 = k − 1, df2 = ntot − k The Chi-square test Chi-square test statistic: χ2 0 = ∑ all cells in the table (observed − expected)2 expected Expected count in cell (i, j) = RiCj n df = (I − 1)(J − 1) Regression Fitted least-squares regression line: ŷ = β̂0 + β̂1x Inference about the intercept, β0, and the slope, β1: df = n− 2 ANSWER SHEET FOLLOWS Page 2 Tables and Formulae Page 2
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