Recitation Practice Problems One-Way ANOVA Part I 1. The average amount of time required to complete a particular task in an assembly process needs to be estimated. Twelve workers were randomly selected to complete the task. The time required (in minutes) by each of the 12 workers was carefully measured and recorded. To ease the calculation burden, we’ll pretend that the times required were all exact to a minute. Data: 10 3 5 5 4 9 7 5 10 5 6 3 Calculate the 95% confidence interval estimate of the mean time required to complete the task. Identify the margin of error. Work: Answer: 6 ± 1.580 CI: (4.420, 7.580) Suppose that this one task can be done with 3 machine types: Machine A, Machine B, or Machine C. Suppose further that the 12 workers were randomly assigned to do the task with one of the 3 machines. The collected times can now be summarized as follows: Machine CMachine BMachine A109876543DataIndividual Value Plot of Machine A, Machine B, Machine C Terminology: Match the term in Column 1 with the correct item in column 2 Column 1 (Term) Column 2 (Item) Response Variable Worker Factor 4 N 3 Treatment Time to complete the task Experimental Unit Type of machine I 12 n1 Machine A Machine A Machine B Machine C 5 6 10 3 4 10 3 5 7 5 5 9 Ax= 4 Bx= 5 Cx= 9 2As= 1.333 2Bs= 0.667 2Cs= 2.000 sA = 1.155 sB = 0.816 sC = 1.414 1818.61168,62 sxRecitation Practice Problems One-Way ANOVA Part I Calculations: Complete the One-way ANOVA Summary Table ANOVA Summary Table: Source of Variation DF Sum of Squares (SS) Mean Squares (MS) F-ratio Between Within Total Check your answers: Hypotheses: State the null and alternative hypotheses for the One-way ANOVA test to determine if the time required to complete the task, on average, is not the same with all 3 machine types. H0: Ha: Decision Rule: Draw the completely labeled decision rule using a 5% significance level. Decision: Reject H Conclusion: Given the ANOVA, calculate the 95% CI to estimate the mean time required to complete the task with Machine C. Identify the margin of error. Work: Answer: 9 ± 1.306 CI: (7.694, 10.306) One-way ANOVA: Machine A, Machine B, Machine C Source DF SS MS F P Factor 2 56.00 28.00 21.00 0.000 Error 9 12.00 1.33 Total 11 68.00 S = 1.155 R-Sq = 82.35% R-Sq(adj) = 78.43%Recitation Practice Problems One-Way ANOVA Part I 2. In a completely randomized design, 12 experimental units were assigned to the first treatment, 15 units to the second treatment, and 18 units to the third treatment. Complete the One-way ANOVA summary table. 3. A one-way ANOVA on the response variable X is performed using samples taken from four populations. The populations and the sampling scenarios are defined below. Group Population Distribution Sample 1 X ~ N(200, 10) SRS with n1 = 16 2 X ~ N(210, 10) SRS with n2 = 25 3 X ~ N(220, 10) SRS with n3 = 25 4 X ~ N(230, 10) SRS with n4 = 36 The MSE from this one-way ANOVA could reasonably be which of the following? a. 215 b. 11 c. 107 d. Cannot be determined without more information. 4. Below are the three Tukey HSD confidence intervals for a comparison of three treatment means. What conclusion do you reach from these intervals? 1 - 2: (8.23, 20.97) 1 - 3: (23.4, 36.2) 2 - 3: (8.8, 21.6) A. 1 = 2 = 3 B. 1 > 2 and 2 = 3 C. 1 > 2 > 3 D. 1 < 2 < 3 E. None of the above Source of Variation SS df MS F Treatments 9 Error 35