STA 6166 – Exam 3 – Fall 2011 PRINT Name _________________________Note: Conduct all tests at = 0.05 significance level.Q.1. A Randomized Complete Block Design was conducted to compare 3 energy drinks in terms of endurance in 6 subjects (each subject drinks each energy drink). The response is time to exhaustion on a treadmill. Due to some outlying observations, use Friedman’s test to determine whether the 3 energy drinks differ in their effects on endurance.p.1.a. Compute the test statistic.Test Statistic = ________________________________________p.1.b. Give the Rejection Region ________________________________Q.2. An experiment was conducted to study the effect of background music on crew productivity. There were 5 music types (treatments), 5 weeks for the study, and 5 days of the week (Monday-Friday). The design involved each music type occurring once each week, and once on each day of the week. Complete the following ANOVA table, and test for differences among the music type effects on productivity based on a latin square design.Q.3. A hotel is interested in studying the effects of washing machines and detergents on whiteness of bed sheets.The hotel has 4 washing machines and 3 brands of detergent. They randomly assign n=4 sheets for each combination of machine and detergent (each sheet is only observed for one combination of machine and detergent). After washing, the sheets are measured for whiteness (high scores are better). p.3.a. Complete the ANOVA table.p.3.b. Is there a significant interaction between Machine and Detergent on whiteness scores? Yes / Nop.3.c. Is there a significant main effect for Machines? Yes / Nop.3.d. Is there a significant main effect for Detergents? Yes / NoQ.4. For each of the following designs, compute Bonferroni’s minimum significant difference.p.4.a. Latin square design, with t=5 treatments and MSE=250.p.4.b. 2-Way ANOVA (a=3,b=4), conducted in a Completely Randomized Design with n=3 replicates per treatment, with MSE=600. Compute Bij for main effects of Factor A (interaction was not significant).Q.5. A manufacturer wishes to compare defective rates of two suppliers of a component used in their product. Let 1 be the true defective rate for supplier 1, and 2 be the true defective rate for supplier 2. The engineering department samples 500 parts from each supplier (n1 = n2 = 500). For supplier 1, X1 = 60 parts were defective, while for supplier 2, X2 = 25 parts were defective.p.5.a. Compute a 95% Confidence Interval for the difference in true probabilities of defective parts for the 2 suppliers: 1 - 2:p.5.b. Based on your interval, which is the best statement?i. Higher defect rate for supplier 1 ii. Lower defect rate for supplier 1 iii. No significant difference Q.6. The following contingency table gives the results of a ballot order experiment on voters’ choice.p.6.b. Give the test statistic for testing whether vote cast (party) is independent of order of party on the ballot.p.6.c. Rejection Region: _________________________________p.6.d. The researchers claim that this study is evidence that ballot order “influences” candidate choice. Based onthis study, the researchers are: Correct or Incorrect ?p.6.a. Complete the Expected and Chi-Square tables (note you just need to compute the upper left-hand corners of the
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