Statistical Analysis HW03: One-Way ANOVA and Confidence Intervals - Prof. Xiaomi Hu, Assignments of Statistics

Download Statistical Analysis HW03: One-Way ANOVA and Confidence Intervals - Prof. Xiaomi Hu and more Assignments Statistics in PDF only on Docsity! Stat 875 HW03 1. p118 3.24 (a) • H0 : µ1 = µ2and µ1 = µ3 H1 : At least one equation in H0 is false • Test Statistic F = MSMMSE • p-value: P (F (2, n− 3) > Fob) • From samples Fob = 38.34, p-value: P (F (2, 12) > 38.34) < 0.0001 • Reject H0 (b) (Revised) Do the contrast test H0 : µ2 = µ3 • H0 : µ2 = µ3 H1 : µ2 6= µ3 • Test Statistic F = MSCMSE • p-value: P (F (1, n− 3) > Fob) • From samples Fob = 70.67, p-value: P (F (1, 12) > 70.67) < 0.0001 • Reject H0 (c) (Second part only) Find a 99% confidence interval for µ2 − µ3 Y 2 − Y 3 ± t0.005(n− 3) √ MSE( 1n2 + 1 n3 ) = 79.4− 100.4± 3.055 √ 15.6 · 25 = −21± 7.631 = (−28.631, −13.369) is a 99% confidence interval for µ2 − µ3. i 1 2 3 ni 5 5 5 Y i 95.2 79.4 100.4 Source DF SS MS F p Model 2 1196.1 598.1 38.34 < 0.0001 Error 12 187.1 15.6 C. Total 14 1383.1 Contrasts 1 1102.5 1102.5 70.67 < 0.0001 1