(Solved): HOMEWORK (ONE-WAY ANOVA) PROB. AND STAT. FOR ENG. (STAT:2020; BOGNAR) MAY 6, 2022 NAME: SECTION: 1 ...

HOMEWORK (ONE-WAY ANOVA) PROB. AND STAT. FOR ENG. (STAT:2020; BOGNAR) MAY 6, 2022 NAME: SECTION: 1. A watch maker wanted to compare four robotic milling machines for cut roughness. The roughness is measured in microns (1/1000 of a mm). After milling a number of parts on each machine, he summarized the data in the following table. Mach 1 Mach 2 Mach 3 Mach 4 n2 = 5 n3 = 6 I1 = 11.5 12 = 8.9 I3 = 9.3 24 = 12.2 84 = 1.1 Assume the roughness for Machine i follows a N(Mi, 0}) distribution, i = 1, 2, 3, 4, and assume that 01 = 02 = 03 = 04. ni = 5 n4 = 6 81 = 1.3 82 = 1.5 83 = 1.0 (a) Find the between groups variance, S. Show your work using clear notation. (b) Find the within groups variance, Sû. Show your work using clear notation. (c) Test Ho: M1 = H2 = M3 = My vs H, : not H, at the a = 0.05 significance level using a 3-step one-way ANOVA test. Find the test statistic and critical value (use Matt's super sweet F-distribution web/phone app to find the critical value), plot the rejection region (be sure to label the distribution), and state your decision and final conclusion. Show your work using clear notation.