Exam 19: Further Non-Parametric Tests

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 is the p-value of the test statistic using a 5% level of significance?

Instruction 19-7 An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants all three varieties of the seeds on each of five different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomised block design,the results are presented in the table that follows. 1elds Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 Below is the Minitab output of the Friedman rank test: Friedman Test: Yield versus Varieties, Fields Friedman test for Yield by Varieties blocked by Fields $\mathrm { S } = 10.00 \mathrm { DF } = 2 \mathrm { P } = 0.007$ Est Sum of Varieties Median Ranks Smith 5 13.500 5.0 Trevor 5 15.667 10.0 Walsh 5 18.533 15.0 Grand median = 15.900 -Referring to Instruction 19-7,what are the degrees of freedom of the Friedman rank test for the difference in the medians at a level of significance of 0.01?

The McNemar test is approximately chi-square distributed.

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 perfume manufacturer will

For the Wilcoxon rank sum test,the quantity T₁ is defined as

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 the 5 blocks are independent so that the yields in one block have no influence on the yields in any other block.

If the assumptions of the one-way ANOVA F test are not met,which of the following test could be used?

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.Which test should she use?

The sum of ranks in a Wilcoxon rank sum test must equal

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,to use the chi-square critical value for the Kruskal-Wallis test,the sample size in each group has to be greater than ________.

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 decision made at a 0.01 level of significance on the Friedman rank test for the difference in medians implies that the 3 medians are not all the same.

The McNemar test is approximately distributed as a standardised normal random variable.

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 decision rule for a level of significance of 0.05 using the Kruskal-Wallis test is to reject the null hypothesis if the test statistic H is ________ assuming that the sample sizes are large enough to use a chi-square approximation.

Instruction 19-7 An agronomist wants to compare the crop yield of three varieties of chickpea seeds.She plants all three varieties of the seeds on each of five different patches of fields.She then measures the crop yield in bushels per acre.Treating this as a randomised block design,the results are presented in the table that follows. 1elds Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 Below is the Minitab output of the Friedman rank test: Friedman Test: Yield versus Varieties, Fields Friedman test for Yield by Varieties blocked by Fields $\mathrm { S } = 10.00 \mathrm { DF } = 2 \mathrm { P } = 0.007$ Est Sum of Varieties Median Ranks Smith 5 13.500 5.0 Trevor 5 15.667 10.0 Walsh 5 18.533 15.0 Grand median = 15.900 -Referring to Instruction 19-7,what is the critical value of the Friedman rank test for the difference in the medians at a level of significance of 0.01?

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 decision made at a 0.01 level of significance on the Friedman rank test for the difference in medians implies that all 3 medians are significantly different.

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.She should reject the null hypothesis using a 5% level of significance.

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 alternative hypothesis of the Kruskal-Wallis test is that ________.

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.She should reject the null hypothesis using a 5% level of significance.

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 rank of the absolute difference for the last pair of observations?

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 is the value of the test statistic using a 5% level of significance?