# report as an Excel file. Solve each problem on a separate tab (worksheet). Organize your solutions on the Excel worksheet properly.

HW Problems: 1. In a completely randomized design, 10 experimental units were used for the first treatment, 12 for the second treatment, and 19 for the third treatment. Sum of Squares due to Treatments and Sum of Squares Total is computed as 1100 and 1700 respectively. Prepare the ANOVA table and complete the same (fill out all the cells). State the Hypotheses. At a .05 level of significance, is there a significant difference between the treatments? Use both p-Value and Critical-Value approaches. 2. To study the effect of temperature on yield in a chemical process, four batches were produced at each of three temperature levels. The results follow. Construct an analysis of variance table. State the Hypotheses. Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process. Use both p-Value and Critical-Value approaches. 3. The following data are from an experiment designed to investigate the perception of corporate ethical values among individuals specializing in marketing (higher scores indicate higher ethical values). State the Hypotheses. a. Use α = .10 to test for significant differences in perception among the three groups. Use both p-Value and Critical-Value approaches. b. Can we conclude that there are differences in the perceptions for marketing managers, marketing research specialists, and advertising specialists. Are the conclusions any different between p-Value and Critical-Value approaches? c. Use Fisher’s LSD approach to determine where the differences occur if they do. 4. A study reported in the Journal of the American Medical Association investigated the cardiac demands of heavy snow shoveling. Eight healthy men underwent exercise testing with a treadmill and a cycle ergometer modified for arm cranking. The men then cleared two tracts of heavy, wet snow by using a lightweight plastic snow shovel and an electric snow thrower. Each subject’s heart rate, blood pressure, oxygen uptake, and perceived exertion during snow removal were compared with the values obtained during treadmill and arm- crank ergometer testing. Suppose the following table gives the heart rates in beats per minute for each of the eight subjects. At the .05 level of significance, test for any significant differences. Use both p-Value and Critical-Value approaches. 5. 6. An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/ unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use α = .05. Use both p-Value and Critical-Value approaches. 7. Type of Ride Roller Coaster Screaming Demon Log Flume Method 1 41 52 50 43 44 46 49 46 48 Method 2 49 50 48 51 46 44 47 48 46 8. A research firm tests the miles-per-gallon characteristics of three brands of gasoline. Automobiles were randomly subjected to treatments and the results of the experiment (in miles per gallon) are presented below. Please note that in this problem raw data is not provided – you would not need it as partial results are already provided. You will be able to use the partial results to solve the problem and answer the questions. The five automobile types are suspected to introduce “Heterogeneity” as gasoline brands are expected to performance differently in different automobile types. The experimenter would prefer to remove any corruptive effect of heterogeneity to get clean results on Gasoline Brands. Hence the analysis is performed in two phases. Gasoline Brands Average X Y Z Automobile Type A … … … 23.67 B … … … 20.33 C … … … 25.00 D … … … 27.00 E … … … 32.33 Average 24.40 26.80 25.80 In Phase I of the analysis on the above data, the following partial ANOVA results were obtained. Source DF SS MS F Gasoline Brand 14.5 Error Total 14 267.3 a) Complete the above ANOVA Table. b) What experimental design was considered for the analysis under Phase I? c) State the Null and Alternate Hypotheses. Customize your hypothesis to the business problem context (do not use generic terms). d) Determine Critical value. Conduct a Critical-value based Hypothesis test (at α = 0.10). What is your decision on the Hypothesis test? e) State your conclusion (what meaning the decision under part ‘d’ carries in the problem context) In phase II of the analysis of the test data, the following partial ANOVA results were obtained. Source DF SS MS F Automobile Type Gasoline Brand 14.5 Error 15.5 Total 14 267.3 f) Complete the above ANOVA Table. g) What experimental design was considered for the analysis under Phase II? h) Is a Hypothesis Test on the factor “Automobile Type” needed? Why or why not? i) Is Hypothesis Test under Phase II (based on what the user is set out to find in the first place) any different from the one considered for Phase I? j) Determine Critical value. Conduct a Critical-Value based Hypothesis Test (at α = 0.10). k) Is there a significant difference in the mean miles- per- gallon characteristics of the three brands of gasoline based on the Hypothesis test? l) If so, which brand(s) are different from the rest? m) You own all five vehicle types in your fleet use them equally. You are interested in maximizing mpg for your vehicles. Which brand/s of Gasoline would you use and why? n) Comparing analyses under Phase I and Phase II, what advantage Phase II provides if any over Phase I of analysis? o) Which method among Phase I and Phase II provides the correct method of analysis in the problem context? Why or why not? 4