Assignment 2 1) DAY TREATMENT TOTALS

Transcription

1 Assignment 2 1) DAY BATCH TOTAL 1 A=8 B=7 D=1 C=7 E= C=11 E=2 A=7 D=3 B= B=4 A=9 C=10 E=1 D= D=6 C=8 E=6 B=6 A= E=4 D=2 B=3 A=8 C=8 25 TOTAL TREATMENT TOTALS A B C D E A) Fill in how the data is to be entered into SAS and write the SAS data step. Next write the SAS code to obtain the output on the reverse side. B) Fill in the missing quanities on the reverse side. A-Z DEPENDENT VARIABLE : TIME SOURCE DF SUM OF SQUARES MEAN SQUARE F VALUE MODEL E C G ERROR 12 D F PR>F CORRECTED TOTAL R-SQUARE C.V. ROOT MSE TIME MEAN A B SOURCE DF ANOVA SS F VALUE PR > F BATCH M H K DAY N I L CATALYST O J STUDENT-NEWMAN-TEST FOR VARIATE: TIME NOTE: THIS TEST CONTROLS THE TYPE I EXPERIMENTWISE ERROR RATE UNDER THE COMPLETE NULL HYPOTHESIS BUT NOT UNDER PARTIAL NULL HYPOTHESES ALPHA=0.05 DF=12 MSE= NUMBER OF MEANS CRITICAL RANGE MEANS WITH THE SAME LETTER ARE NOT SIGNFICANTLY DIFFERENT. SNK GROUPING MEAN N CATALYST A P 5 U A Q 5 V B R 5 X B S 5 Y B T 5 Z

2 2) Percentage of Cotton TOTALS A) Fill in how the data is to be entered into SAS and write the SAS data step. Next write the SAS code to obtain the output on the reverse side. B) Fill in the missing quantities on the reverse side. A-P DEPENDENT VARIABLE: STRENGTH SOURCE DF SUM OF SQUARES MEAN SQUARE FVALUE MODEL A B C D ERROR E F G CORRECTED TOTAL R-SQUARE C.V. ROOT MSE STRENGTH MEAN H SOURCE DF ANOVA SS F VALUE PR > F PERCENT I J K P T TESTS (LSD) FOR VARIABLE: STRENGTH NOTE: THIS TEST CONTROLS THE TYPE I COMPARISONWISE ERROR RATE. NOT THE EXPERIMENTWISE ERROR RATE ALPHA=0.05 DF=12 MSE= CRITICAL VALUE OF T= LEAST SIGNIFICANT DIFFERENCE= MEANS WITH THE SAME LETTER ARE NOT SIGNIFICANTLY DIFFERENT. SNK GROUPING MEAN N PERCENT L M N O C) Perform a Kruskal-Wallis test on the data with the pairwise comparisons. Do we obtain different results? 3) In 1987, two years after the birth of new Coke and the new-old Coke Classic a New York marketing research firm conducted a study to determine consumer preference for the three brands: new Coke, Coke Classic, and Pepsi. The purpose of the study was to determine how well the two Cokes were selling vis-a-vis their competitor. Although Pepsi is known to sell more in supermarkets, Coke was believed to have a wide lead over Pepsi in vending machine sales. As part of the analysis, the researchers wanted to find out whether the three brands sold about equally well,

3 on a Pepsi machine. A random sample of nine public buildings in Manhattan fitting the requirements was selected. The data (in number of cans sold over a given period of time) are as follow. Building New Coke Coke Classic Pepsi Analyze the data. Threat Building as a block. Perform a multiple comparison on brand. Which is the best selling? Which is the worst selling? Is there any difference? 4) The Manager of fitness center wants to test whether three of her top athletes are of the same average performance level. The center has three identical exercise machines located at different places in the exercise hall. There are also three daily exercise times: morning, noontime, and evening. The manager assigns each of the athletes to a machine and to an exercise time according to the randomly chosen Latin square that follows. The manager measures the athletes' performance (number of pullups they can do in a specified time period.) The athletes are labeled A, B and C. Given the data in the Latin square, do all three athletes have the same average performance level? Machine Time Morning B=24 A=31 C=30 Noon C=22 B=29 A=33 Evening A=30 C=26 B=32 5) Recently, the competition between Kodak and Fuji has been intensifying. Kodak has reportedly been analyzing films made by Fuji to determine the secrets of Fuji's bright colors. As part of an analysis, a random sample of five pieces of film by Kodak were developed by a process we will denote as process A, another random sample of five Kodak films were developed by process B, and a third sample by process C. The same was done with three sets of five pieces of film by Fuji. Also, as a third comparison for control, three sets of five pieces of film by Agfa were developed. All the developed films were photochemically tested for color brightness. The results were analyzed by two-way ANOVA aimed at determining whether color brightness differences existed among the three developing processes and among the three kinds of film. Kodak was also interested in finding in the following table (the higher the score, the brighter the colors). Process Film A B C Kodak 32,34,31,30,37 26,29,27,30,31 28,28,27,30,32 Fuji 43,41,44,50,47 32,38,38,40,36 32,32,36,35,34 Agfa 23,24,25,21,26 27,30,25,25,27 25,27,26,22,25 Make sure you construct an interaction plot for the interaction between process and film brand. Perform a multiple comparison on both main effects.

4 6) Problem 7-52 of text. Test the assumption of normality of each population (PROC UNIVARIATE), and test the assumption of equal variance (PROC TTEST). Perform both the parametric and nonparametric test irrespective of the results of the assumption checks. Which is the best procedure of this problem and why? 7) Problem of text. Do the same as specified in problem 8. 8) Problem of text. Do both the parametric and nonparametric procedure. Which is more appropriate?

5 9) Case Two.

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