# OSU BUSMGT 2320 - Recitation Practice Problems One-Way ANOVA Part I (3 pages)

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## Recitation Practice Problems One-Way ANOVA Part I

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- School:
- Ohio State University
- Course:
- Busmgt 2320 - Decision Sciences: Statistical Techniques

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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 x 6 s 2 68 11 6 1818 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 2 A Machine B 6 4 5 5 xB 5 2 B Machine C 10 10 7 9 xC 9 2 C 1 333 s 0 667 s 2 000 sA 1 155 sB 0 816 sC 1 414 s Individual Value Plot of Machine A Machine B Machine C 10 9 8 Data Machine A 5 3 3 5 xA 4 7 6 5 4 3 Machine A 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 B Machine C Recitation Practice Problems One Way ANOVA Part I Calculations Complete the One way ANOVA Summary Table ANOVA Summary Table Source of Variation Sum of Squares SS DF Mean Squares MS F ratio Between Within Total Check your answers One way ANOVA Machine A Machine B Machine C Source Factor Error Total DF 2 9 11 S 1 155 SS 56 00 12 00 68 00 MS 28 00 1 33 R Sq 82 35 F 21 00 P 0 000 R Sq adj 78 43 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 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 Source of Variation SS df MS Treatments F 9 Error 35 Total 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 A 1 2 3 B 1 2 and 2 3 C 1 2 3 D 1 2 3 E None of the above 1 3 23 4 36 2 2 3 8 8 21 6

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