10_23 - STAT 420 Examples for 10/23/2007 Fall 2007 ANOVA...

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Unformatted text preview: STAT 420 Examples for 10/23/2007 Fall 2007 ANOVA (Analysis of Variance) Population 1 Population 2 Population I mean 1 std. dev. mean 2 std. dev. mean I std. dev. & & & y 1 1 , y 1 2 , , y 1 n 1 y 2 1 , y 2 2 , , y 2 n 2 y I 1 , y I 2 , , y I n I 1 y , s 1 2 2 y , s 2 2 I y , s I 2 H : 1 = 2 = = I H 1 : not all of the i are equal. ( We want to test simultaneously for differences among the means of all I populations. ) Example : There is a great deal of interest in comparing the mileage rating of different makes of automobiles. Other things being equal, customers buy car that gets the best mileage. Suppose we wish to compare the mean fuel consumption for I = 3 different makes of automobile, Car 1, Car 2, and Car 3. Suppose 5 cars of each make are selected randomly and the gasoline mileage (in miles per gallon) is recorded for each car. Suppose that 1 y = 19.0, 2 y = 20.4, 3 y = 21.8. Is there enough evidence that the mean fuel consumption is not the same for Car 1, Car 2 and Car 3? Data Set A: Car 1 Car 2 Car 3 18.2 19.4 19.6 19.0 18.8 19.8 21.0 20.0 20.8 20.4 21.2 21.8 22.4 22.0 21.6 Sample mean 19.0 20.4 21.8 Sample std. dev. 0.5477 0.5099 0.4472 Sample variance 0.300 0.260 0.200 Data Set B: Car 1 Car 2 Car 3 17.0 20.4 24.0 15.8 17.8 24.2 22.0 17.8 16.2 21.8 26.0 19.8 24.4 16.0 22.8 Sample mean 19.0 20.4 21.8 Sample std. dev. 3.26 3.29 3.97 Sample variance 10.66 10.84 15.76 The Analysis of Variance Idea:...
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This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.

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10_23 - STAT 420 Examples for 10/23/2007 Fall 2007 ANOVA...

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