Tests of Homogeneity and Independence Robb T Koether Homework Review Homogeneous Populations Tests of Homogeneity and Independence Lecture 50 Sections 14 4 14 5 Independent Variables Mendel s Experiments Assignment Robb T Koether Hampden Sydney College Wed Apr 22 2009 Outline Tests of Homogeneity and Independence Robb T Koether Homework Review 1 Homework Review 2 Homogeneous Populations 3 Independent Variables 4 Mendel s Experiments 5 Assignment Homogeneous Populations Independent Variables Mendel s Experiments Assignment Exercise 14 7 page 935 Tests of Homogeneity and Independence Robb T Koether Homework Review Homogeneous Populations Independent Variables Exercise 14 7 page 935 An experiment is conducted to try to determine the most effective over the counter pain relief medication The five best selling brands of pain relief are tested on n 200 randomly selected subjects Mendel s Experiments For each subject the best pain relief medicine is recorded based on various criteria Assignment The results are presented below You are asked to test the claim that the five brands K 5 of pain relief medicine are equally effective Exercise 14 7 page 935 Tests of Homogeneity and Independence Robb T Koether Homework Review Exercise 14 7 page 935 Homogeneous Populations Independent Variables Mendel s Experiments Assignment Observed Counts Brand of Pain Relief A B C D E 38 44 56 37 25 Exercise 14 7 page 935 Tests of Homogeneity and Independence Robb T Koether Exercise 14 7 page 935 Homework Review a State the null hypothesis Homogeneous Populations b Compute the expected counts Independent Variables Mendel s Experiments Assignment c Compute the observed test statistic d Find the p value e State your decision and conclusion using a 5 significance level Exercise 14 7 page 935 Tests of Homogeneity and Independence Robb T Koether Homework Review Homogeneous Populations Independent Variables Mendel s Experiments Assignment Solution a If the brands are equally effective then we would expect them to be selected equally often as best by the subjects Therefore H0 p1 p2 p3 p4 p5 0 20 b The sample size is n 200 so the expected counts are each 40 Exercise 14 7 page 935 Tests of Homogeneity and Independence Robb T Koether Homework Review Homogeneous Populations Independent Variables Mendel s Experiments Assignment Solution c The test statistic is 2 P all cells O E 2 E Its value is 38 40 2 44 40 2 56 40 2 40 40 40 4 16 256 9 225 40 40 40 40 40 510 40 12 75 2 37 4 40 Exercise 14 7 page 935 Tests of Homogeneity and Independence Robb T Koether Homework Review Solution Homogeneous Populations d The p value is 2 cdf 12 75 E99 4 0 0126 Independent Variables e Reject H0 and conclude that the brands of pain reliever are not equally effective Mendel s Experiments Assignment Homogeneous Populations Tests of Homogeneity and Independence Robb T Koether Homework Review Homogeneous Populations Independent Variables Mendel s Experiments Assignment Now we wish to compare two or more populations by observing the values of a qualitative variable for each of them For example is the distribution of types of crime in Richmond the same in 2009 as it was in 2008 Jan Mar Category Homicide Rape Robbery Assault Arson Burglary Larceny Auto Theft 2008 11 10 135 132 21 334 930 234 2009 9 8 150 143 10 284 1032 208 Homogeneous Populations Tests of Homogeneity and Independence Robb T Koether Homework Review Homogeneous Populations Independent Variables Mendel s Experiments Assignment Now we wish to compare two or more populations by observing the values of a qualitative variable for each of them For example is the distribution of types of crime in Richmond the same in 2009 as it was in 2008 Jan Mar Category Homicide Rape Robbery Assault Arson Burglary Larceny Auto Theft 2008 11 10 135 132 21 334 930 234 2009 9 8 150 143 10 284 1032 208 Homogeneous Populations Tests of Homogeneity and Independence Robb T Koether Homework Review Homogeneous Populations Independent Variables Mendel s Experiments Assignment Now we wish to compare two or more populations by observing the values of a qualitative variable for each of them For example is the distribution of types of crime in Richmond the same in 2009 as it was in 2008 Jan Mar Category Homicide Rape Robbery Assault Arson Burglary Larceny Auto Theft 2008 11 10 135 132 21 334 930 234 2009 9 8 150 143 10 284 1032 208 Homogeneous Populations Tests of Homogeneity and Independence Robb T Koether Definition Homogeneous Homework Review Homogeneous Populations Independent Variables Mendel s Experiments Assignment Two populations are called homogeneous if they exhibit the same distributions over the same categories If there was no significant change in the distribution of types of crime in Richmond then those two populations 2008 2009 are homogeneous The Test of Homogeneity Tests of Homogeneity and Independence Robb T Koether Homework Review Homogeneous Populations Independent Variables Mendel s Experiments Assignment The null hypothesis is that the populations are homogeneous The alternative hypothesis is that the populations are not homogeneous H0 The populations are homogeneous H1 The populations are not homogeneous Independent Variables Tests of Homogeneity and Independence Robb T Koether Homework Review Homogeneous Populations Independent Variables Mendel s Experiments Assignment In single vehicle fatal accidents in 2007 consider the following two variables Whether the driver was alcohol impaired The time of day or night Time 12am 3am 3am 6am 6am 9am 9am 12pm 12pm 3pm 3pm 6pm 6pm 9pm 9pm 12am AlcoholImpaired 2496 1221 343 182 332 635 1189 1616 Not AlcoholImpaired 1337 1100 1507 1421 1906 2203 2337 1924 Independent Variables Tests of Homogeneity and Independence Robb T Koether Homework Review Homogeneous Populations Independent Variables Mendel s Experiments Assignment In single vehicle fatal accidents in 2007 consider the following two variables Whether the driver was alcohol impaired The time of day or night Time 12am 3am 3am 6am 6am 9am 9am 12pm 12pm 3pm 3pm 6pm 6pm 9pm 9pm 12am AlcoholImpaired 2496 1221 343 182 332 635 1189 1616 Not AlcoholImpaired 1337 1100 1507 1421 1906 2203 2337 1924 Independent Variables Tests of Homogeneity and Independence Robb T Koether Homework Review Homogeneous Populations Independent Variables Mendel s Experiments Assignment In single vehicle fatal accidents in 2007 consider the following two variables Whether the driver was alcohol impaired The time of day or night
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