Week6HW

# Week6HW - EC315 Week 6 Homework Chapter 12, Question 22 A...

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EC315 Week 6 Homework Chapter 12, Question 22 A physician who specializes in weight control has three different diets she recommends. As an experiment, she randomly selected 15 patients and then assigned 5 to each diet. After three weeks the following weight losses, in pounds, were noted. At the .05 significance level, can she conclude that there is a difference in the mean amount of weight loss among the three diets? Plan A Plan B Plan C 5 6 7 7 7 8 4 7 9 5 5 8 4 6 9 H o : μ 1 = 2 = 3 H 1 : Not all means are equal α = 0.05 H o is rejected if F > 3.89 Degrees of Freedom = 2/12 from the ANOVA table X=EX/n=5+7+4+5+4/5=5 X=EX/n=6+7+7+5+6/5=6.2 X=EX/n=7+8+9+8+9/5=8.2 Not all means are equal Test Statistic = 13.52 from the ANOVA table Source SS df MS F Treatme nt 26.13 2 13.06 7 13.52 Error 11.60 12 0.967 Total 37.73 14 H o is rejected since 13.52 > 3.89 There is a difference in the mean weight loss.

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Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of six hourly periods is chosen for each assembly line and the number of components produced during these periods for each line is recorded. The output from a statistical software package is: Summary Groups Count Sum Average Variance Line A 6 250 41.66667 0.266667 Line B 6 260 43.33333 0.666667 Line C 6 249 41.5 0.7 ANOVA Source of Variation SS df MS F p -value Between Groups 12.33333 2 6.166667 11.32653 0.0010 05 Within Groups 8.166667 15 0.544444 Total 20.5 17 A) Use a .01 level of significance to test if there is a difference in the mean production of the three assembly lines. H o : μ = = H 1 : Not all means are equal α = 0.01 H o is rejected if F > 6.36 Degrees of Freedom = 2/15 from the ANOVA table Test Statistic = 11.32653 from the ANOVA table H o is rejected because 11.32653 > 6.36 Since p-value in the table is 0.001005, which is less than significant level 0.01, we can also reject the null hypothesis.
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## This note was uploaded on 10/07/2011 for the course EC 315 taught by Professor Barcus during the Spring '10 term at Park.

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Week6HW - EC315 Week 6 Homework Chapter 12, Question 22 A...

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