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Unformatted text preview: 1 Exercises for Chapter 10 1. Porous carbon materials are used commercially in several industrial applications, including gas separation, membrane separation, and fuel cell applications ( J. Phys. Chem. B , 1997, 101 , 3988; Microporous Mater , 1994, 4 , 407; Nature , 2001, 412 , 169). For the purpose of gas separation, the pore size distribution is important. An experiment conducted to compare the pore size distribution when the carbon is made at four different temperatures (300 o C, 400 o C, 500 o C, and 600 o C) yielded the following results: 300 : 7.75 7.0 6.9 7.5 8.0 400 : 6.9 7.6 7.0 7.0 7.7 500 : 6.7 6.9 6.9 6.2 6.6 600 : 6.4 6.2 6.0 6.6 6.0 Of interest is to test the hypothesis that the population mean of pore size is the same for all four temperatures, i.e. H : 1 = = 4 vs H a : H is not true. a) What assumptions, if any, are needed for the validity of the ANOVA F-test? b) Conduct the F-test at level = 0 . 05. c) Perform Tukeys multiple method to determine which methods are (statistically) signifi- cantly different. 2. Records of teaching an honors statistics class in Experimental Design for engineers, indicated that different Professors had adopted one of three different teaching methods: A) Use of a textbook as the main source of teaching material, B) Use of a textbook combined with com- puter activities, and C) Use of specially designed instructional notes together with computer activities. It was decided to compare the three teaching methods by randomly dividing twelve students in three groups of four, to receive each of the three teaching methods. A common exam was administered in the end. The scores for the three groups were A: 74 76 68 72 B: 73 78 75 80 C: 92 82 85 86 Of interest is to test the hypothesis that the three methods are equally effective, i.e. H : 1 = 2 = 3 vs H a : H is not true. a) What assumptions, if any, are needed for the validity of the ANOVA F-test? b) Conduct the F-test at level = 0 . 05. c) Perform Tukeys multiple method to determine which methods are (statistically) signifi- cantly different. 3. Consider the setting and data of Exercise 1....
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This note was uploaded on 01/11/2012 for the course STAT 401 taught by Professor Akritas during the Fall '00 term at Pennsylvania State University, University Park.
- Fall '00