Exam 12: Chi-Square and Nonparametric Tests

SCENARIO 12-5 Four surgical procedures currently are used to install pacemakers.If the patient does not need to return for follow-up surgery,the operation is called a "clear" operation.A heart center wants to compare the proportion of clear operations for the 4 procedures,and collects the following numbers of patients from their own records: Procedure They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05. -Referring to Scenario 12-5,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure A and procedure C using a 0.05 level of significance?

SCENARIO 12-3 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: She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05. -Referring to Scenario 12-3,the expected cell frequency in the Male/Local cell is .

SCENARIO 12-13 Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-yearolds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the mean number of hours spent watching TV and weights are independent at 1% level of significance. -Referring to Scenario 12-13,the value of the test statistic is

SCENARIO 12-11 The director of admissions at a state college is interested in seeing if admissions status (admitted,waiting list,denied admission)at his college is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table: He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Scenario 12-11,the null hypothesis claims that "there is no association between admission status at the college and the type of community in which an applicant resides."

SCENARIO 12-10 One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced.The quality control department wants to find out whether there is a relationship between years of experience and defect rate.Since the job is repetitious,after the initial training period any improvement due to a learning effect might be offset by a loss of motivation.A defect rate is calculated for each worker in a yearly evaluation.The results for 100 workers are given in the table below. -Referring to Scenario 12-10,which test would be used to properly analyze the data in this experiment to determine whether there is a relationship between defect rate and years of experience?

To use the Wilcoxon Rank Sum Test as a test for location,you must assume that

SCENARIO 12-17 Three new different models of compact SUVs have just arrived at the market.You are interested in comparing the gas mileage performance of all three models to see if they are the same.A partial computer output for twelve compact SUVs of each model is given below: You are told that the gas mileage population distributions for all three models are not normally distributed. -Referring to Scenario 12-17,what is your decision on the test using a 5% level of significance?

The Kruskal-Wallis Rank Test for differences in more than two medians is a nonparametric alternative to

SCENARIO 12-5 Four surgical procedures currently are used to install pacemakers.If the patient does not need to return for follow-up surgery,the operation is called a "clear" operation.A heart center wants to compare the proportion of clear operations for the 4 procedures,and collects the following numbers of patients from their own records: Procedure They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05. -Referring to Scenario 12-5,there is sufficient evidence to conclude that the proportions between procedure C and procedure D are different at a 0.05 level of significance.

SCENARIO 12-14 A perfume manufacturer is trying to choose between 2 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 the more expensive layout to 4 groups and determines the approval rating for each group.He presents the "scratch-and-sniff" layout to 5 groups and again determines the approval rating of the perfume for each group.The data are given below.Use this to test the appropriate hypotheses with the Wilcoxon Rank Sum Test with a level of significance of 0.05. 12-34 Chi-Square and Nonparametric Tests -Referring to Scenario 12-14,the perfume manufacturer will

SCENARIO 12-10 One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced.The quality control department wants to find out whether there is a relationship between years of experience and defect rate.Since the job is repetitious,after the initial training period any improvement due to a learning effect might be offset by a loss of motivation.A defect rate is calculated for each worker in a yearly evaluation.The results for 100 workers are given in the table below. -Referring to Scenario 12-10,a test was conducted to determine if a relationship exists between defect rate and years of experience.Which of the following p-values would indicate that defect rate and years of experience are dependent? Assume you are testing at α = 0.05.

SCENARIO 12-11 The director of admissions at a state college is interested in seeing if admissions status (admitted,waiting list,denied admission)at his college is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table: He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Scenario 12-11,the expected cell frequency for the Admitted/Urban cell is .

When using the $\chi$ ² tests for independence,you should be aware that expected frequencies that are too small will lead to a large Type I error.

SCENARIO 12-15 Two new different models of compact SUVs have just arrived at the market.You are interested in comparing the gas mileage performance of both models to see if they are the same.A partial computer output for twelve compact SUVs of model 1 and thirteen of model 2 is given below: You are told that the gas mileage population distributions for both models are not normally distributed. -Referring to Scenario 12-15,what is your conclusion on the test using a 5% level of significance?

SCENARIO 12-17 Three new different models of compact SUVs have just arrived at the market.You are interested in comparing the gas mileage performance of all three models to see if they are the same.A partial computer output for twelve compact SUVs of each model is given below: You are told that the gas mileage population distributions for all three models are not normally distributed. -Referring to Scenario 12-17,what is the value of the Kruskal-Wallis test statistic?

SCENARIO 12-6 According to an article in Marketing News,fewer checks are being written at the grocery store checkout than in the past.To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance,the results of a survey of 500 shoppers in three consecutive years are obtained and presented below. -Referring to Scenario 12-6,there is insufficient evidence to conclude that the proportions between year 1 and year 3 are different at a 0.05 level of significance.

SCENARIO 12-11 The director of admissions at a state college is interested in seeing if admissions status (admitted,waiting list,denied admission)at his college is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table: He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Scenario 12-11,the alternative hypothesis claims that "there is some connection between admission status at the college and the type of community in which an applicant resides."

SCENARIO 12-14 A perfume manufacturer is trying to choose between 2 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 the more expensive layout to 4 groups and determines the approval rating for each group.He presents the "scratch-and-sniff" layout to 5 groups and again determines the approval rating of the perfume for each group.The data are given below.Use this to test the appropriate hypotheses with the Wilcoxon Rank Sum Test with a level of significance of 0.05. 12-34 Chi-Square and Nonparametric Tests -Referring to Scenario 12-14,the null hypothesis should be rejected.

SCENARIO 12-7 Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. At the 0.05 level of significance,you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities. -Referring to Scenario 12-7,the test will involve _____ degrees of freedom.

SCENARIO 12-5 Four surgical procedures currently are used to install pacemakers.If the patient does not need to return for follow-up surgery,the operation is called a "clear" operation.A heart center wants to compare the proportion of clear operations for the 4 procedures,and collects the following numbers of patients from their own records: Procedure They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05. -Referring to Scenario 12-5,the null hypothesis will be rejected.