STA 6166 – Exam 2 – Fall 2010 PRINT Name ________________________Q.1.: An experimenter is interested in comparing the mean potencies among 3 formulations of insecticides. Shesets up 18 containers, each with 100 specimens. He then randomly assigns the insecticides to the containers, so that each insecticide is used in 6 containers. He measures the numbers of specimens dying for each container. The results are given below.p.1.a. Compute the treatment (formulation) sum of squares and degrees of freedom.p.1.b. Compute the error sum of squares and degrees of freedom.p.1.c. Use Bonferroni’s method to obtain simultaneous 95% Confidence Intervals for differences between population means among the 3 formulations.Bij = Form 1 – Form 2:Form 1 – Form 3:Form 2 – Form 3:p.1.d. Show your results by drawing lines that join means that are not significantly different. 1 2 3Q.2.: An experiment to measure the effects of 2 factors on dye color permanence in fabrics. The researcher is interested in 3 varieties of cotton (Factor A) and 4 brands of detergent (Factor B). He bases his analysis on a 3 replicates for each combination of cotton and detergent, and the response measured is the level of color in fabricspecimen after 10 wash cycles. p.2.a. Complete the ANOVA table, and all tests at the = 0.05 significance level.p.2.b. i. Is there a significant interaction between fabric and detergent? Yes or Nop.2.b. ii. Is there a significant main effect for fabric? Yes or Nop.2.b. iii. Is there a significant main effect for detergent? Yes or Nop.2.c. Compute Bonferroni’s Minimum Significant Differences based on an experiment-wise error rate of E = 0.05 (assuming no interaction):p.2.c.i.: For Fabrics:p.2.c.ii: For Detergents:Q.3. A college’s volleyball coach is interested in whether her team’s players prefer one brand of shoe among 3 brands. She has each player practice wearing each brand (in random order), and has each player rate the comforton a 0-100 visual analogue scale. She analyzes the experiment as a Randomized Block Design with t = 3 treatments (shoe brands) and b = 18 (team players). She obtains the following results from the Analysis of Variance:1 2 365 80 55 225Y Y Y MSE= = = =g g g p.3.a. Use Bonferroni’s method to obtain simultaneous 95% confidence intervals for the population mean ratings differences among all pairs of brands.Bij = Brand 1 – Brand 2:Brand 1 – Brand 3:Brand 2 – Brand 3:p.3.b. Show your results by drawing lines that join means that are not significantly different. 3 1 2Q.4. A study is conducted to compare the defective rates among 3 suppliers of a particular part to an auto manufacturer. A technician randomly samples 100 items from each supplier and she determines whether or not the item is defective. (Conduct the test described below at = 0.05 significance level)p.4.a. Compute her table of expected counts under the hypothesis that probability of a part being defective is independent of supplier. H0: P(Defective|Supplier A) = P(Defective|Supplier B) = P(Defective|Supplier C) p.4. b. Compute her Chi-square statisticp.4.c. Reject / Do not Reject H0 because Test statistic is Larger / Smaller than ______________Q.5. A study compared life-spans among 3 species of plants in lab settings. The researchers determined that the life-spans followed distributions that were clearly not normal. They planted 10 plants from each variety, and measured the time until the plants demonstrated a particular amount of wilting. The life-spans and their ranks are given below. (Conduct the test described below at = 0.05 significance level)p.5.a. Compute the Kruskal-Wallis statistic for testing H0: Species mean life-spans are equal.p.5.b. Reject / Do not Reject H0 because Test statistic is Larger / Smaller than
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