746 APPENDIX A Tables and Formulas (df = smaller of n1 - 1, n2 - 1) (s1 and s2 unknown and not assumed equal) Ch. 9: Confidence Intervals (two populations) 1 pn 1 - p n 22 - E 6 1 p1 - p22 6 1 p n 1 - p n 22 + E where E = za>2Bpn 1q n 1 n1 + pn 2q n 2 n2 1x1 - x22 - E 6 1m1 - m22 6 1x1 - x22 + E (Indep.) where E = ta>2Bs2 1 n1 + s2 2 n2 E = ta>2Bs2 p n1 + s2 p n2 1df = n1 + n2 - 22 s2 p = 1n1 - 12s 2 1 + 1n2 - 12s 2 2 1n1 - 12 + 1n2 - 12 (s1 and s2 unknown but assumed equal) E = za>2B s 2 1 n1 + s 2 2 n2 (s1, s2 known) d - E 6 md 6 d + E (Matched pairs) where E = ta>2 sd1 n 1df = n - 12 Formulas by Mario F. Triola Copyright 2022 Pearson Education, Inc. Ch. 9: Test Statistics (two populations) z = 1pn 1 - p n 22 - 1p1 - p22 Bp q n1 + p q n2 Two proportions p = x1 + x2 n1 + n2 t = 1x1 - x22 - 1m1 - m22 Bs2 1 n1 + s2 2 n2 df = smaller of n1 - 1, n2 - 1 Two means—independent; s1 and s2 unknown, and not assumed equal. t = 1x1 - x22 - 1m1 - m22 Bs2 p n1 + s2 p n2 1df = n1 + n2 - 22 s2 p = 1n1 - 12s 2 1 + 1n2 - 12s 2 2 n1 + n2 - 2 Two means—independent; s1 and s2 unknown, but assumed equal. z = 1x1 - x22 - 1m1 - m22 B s 2 1 n1 + s 2 2 n2 Two means—independent; s1, s2 known. t = d - md sd1 n Two means—matched pairs (df = n - 1) F = s2 1 s2 2 Standard deviation or variance— two populations (where s2 1 Ú s 2 2) Ch. 10: Linear Correlation/Regression Correlation r = nΣxy - 1Σx21Σy2 2 n1Σx22 - 1Σx222n1Σy22 - 1Σy22 or r = g1zx zy2 n - 1 where zx = z score for x zy = z score for y Slope: b1 = nΣxy - 1Σx21Σy2 n 1Σx22 - 1Σx22 or b1 = r sy sx y-Intercept: b0 = y - b1x or b0 = 1Σy21Σx22 - 1Σx21Σxy2 n 1Σx22 - 1Σx22 yn = b 0 + b1x Estimated eq. of regression line r2 = explained variation total variation se = BΣ1y - yn22 n - 2 or BΣy2 - b 0Σy - b1Σxy n - 2 yn - E 6 y 6 yn + E Prediction interval where E = ta>2se B1 + 1 n + n1x0 - x2 2 n1Σx22 - 1Σx22 Ch. 11: Goodness-of-Fit and Contingency Tables x2 = g1O - E22 E Goodness-of-fit (df = k - 1) x2 = g1O - E22 E Contingency table [df = (r - 1)(c - 1)] where E = 1row total21column total2 1grand total2 x2 = 10 b - c0 - 122 b + c McNemar’s test for matched pairs 1df = 12 Ch. 12: One-Way Analysis of Variance Procedure for testing H0: m1 = m2 = m3 = c 1. Use software or calculator to obtain results. 2. Identify the P-value. 3. Form conclusion: If P-value … a, reject the null hypothesis of equal means. If P-value 7 a, fail to reject the null hypothesis of equal means. Ch. 12: Two-Way Analysis of Variance Procedure: 1. Use software or a calculator to obtain results. 2. Test H0: There is no interaction between the row factor and column factor. 3. Stop if H0 from Step 2 is rejected. If H0 from Step 2 is not rejected (so there does not appear to be an interaction effect), proceed with these two tests: Test for effects from the row factor. Test for effects from the column factor.
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