Exam 19: Further Non-Parametric Tests

Instruction 19-6A As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She took three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below. -Referring to Instruction 19-6A,the calculation of the Kruskal-Wallis test statistic H involves obtaining the total of the ranks for each sample.These totals are ________,________,________,and ________.

Instruction 19-5 A perfume manufacturer is trying to choose between two magazine advertising layouts.An expensive layout would include a small package of the perfume.A cheaper layout would include a "scratch-and-sniff" sample of the product.The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate.The manufacturer presents both layouts to five groups and determines the approval rating from each group on both layouts.The data are given below.Use this to test whether the median difference in approval rating is different from zero in favour of the more expensive layout with a level of significance of 0.05. Package Scratch 52 37 68 43 43 53 48 39 56 47 -Referring to Instruction 19-5,what is the value of the test statistic?

Instruction 19-6A As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles.She took three trials of each brand and determined their maximum downhill speeds.The results are presented in kilometres per hour in the table below. -Referring to Instruction 19-6A,the calculation of the Kruskal-Wallis test statistic H involves ranking the observations.Construct a table containing these ranks.

The Wilcoxon rank-sum test is a non-parametric test for testing the difference between two ________ from independent samples.

Given two samples with sizes 20 and 14 respectively,for the Wilcoxon rank sum test the total sample size is

The Journal of Business Venturing reported on the activities of entrepreneurs during the organisation creation process.As part of a designed study,a total of 71 entrepreneurs were interviewed and divided into 3 groups: those that were successful in founding a new firm (n₁ = 34),those still actively trying to establish a firm (n₂ = 21),and those who tried to start a new firm but eventually gave up (n₃ = 16).The total number of activities undertaken (e.g. ,developed a business plan,sought funding,looked for facilities)by each group over a specified time period during organisation creation was measured.The objective is to compare the mean number of activities of the 3 groups of entrepreneurs.Because of concerns over necessary assumption of the parametric analysis,it was decided to use a nonparametric analysis.Identify the nonparametric method that would be used to analyse the data.

Instruction 19-1 The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: Male Female Total Local 27 44 71 Non-Local 33 25 5 Total 60 69 129 She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05. -Referring to Instruction 19-1,the director now wants to know if the proportion of users who are male and the proportion of users who use the local routes are the same.Which test should she use?

Instruction 19-1 The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: Male Female Total Local 27 44 71 Non-Local 33 25 5 Total 60 69 129 She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05. -Referring to Instruction 19-1,the director now wants to know if the proportion of users who are male and the proportion of users who use the local routes are the same.What should be her conclusion?

Instruction 19-4 The director of the MBA program of a university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good.Given below is the result from 215 students' view of the program before and after the orientation. After the Orientation Before the Orientation Good Not Good Total Good 93 37 130 Not Good 71 14 85 Total 164 51 215 -Referring to Instruction 19-4,the Friedman rank test is valid only if there is no interaction between the 5 blocks and the 3 treatment levels.

Instruction 19-5 A perfume manufacturer is trying to choose between two magazine advertising layouts.An expensive layout would include a small package of the perfume.A cheaper layout would include a "scratch-and-sniff" sample of the product.The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate.The manufacturer presents both layouts to five groups and determines the approval rating from each group on both layouts.The data are given below.Use this to test whether the median difference in approval rating is different from zero in favour of the more expensive layout with a level of significance of 0.05. Package Scratch 52 37 68 43 43 53 48 39 56 47 -Referring to Instruction 19-5,the hypotheses that should be used are

Instruction 19-1 The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: Male Female Total Local 27 44 71 Non-Local 33 25 5 Total 60 69 129 She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05. -Referring to Instruction 19-1,the director now wants to know if the proportion of users who are female and the proportion of users who use the local routes are the same.What is the value of the test statistic using a 5% level of significance?