Exam 12: Chi-Square and Nonparametric Tests

SCENARIO 12-16 As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles.She took 3 of each brand and determined their maximum downhill speeds.The results are presented in miles per hour in the table below. -Referring to Scenario 12-16,the sporting goods retailer decided to perform a Kruskal-Wallis test even though the sample size in each of the 4 groups is not larger than 5.The null hypothesis of the test 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 test is always a one-tail test.

SCENARIO 12-9 Many companies use well-known celebrities as spokespersons in their TV advertisements.A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent.Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson.The gender of the spokesperson and whether or not the viewer could identify the product was recorded.The numbers in each category are given below. -Referring to Scenario 12-9,at 5% level of significance,the critical value of the test statistic is

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 B and procedure C are different at a 0.05 level of significance.

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 A and procedure D are different at a 0.05 level of significance.

If the sample sizes in each group is larger than 5,the Kruskal-Wallis rank test statistic can be approximated by a standardized normal distribution.

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 12-12,if the null hypothesis of no connection between time spent watching TV and time spent reading story books is true,how many children watching less than 2 hours of TV and reading no more than 2 hours of story books on average can we expect?

SCENARIO 12-4 A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations.A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations,along with the number of reported errors. The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ. -Referring to Scenario 12-4,at 1% 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 critical value of the Kruskal-Wallis test statistic?

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 B and procedure D using a 0.05 level of significance?

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 sufficient evidence to conclude that the proportions between year 2 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 p-value of this test is greater than 0.01.

SCENARIO 12-2 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day.He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors.In a random sample of 100 of each type of major at graduation,he found that 65 accounting majors and 52 economics majors had job offers.If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05. -Referring to Scenario 12-2,the same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.

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 are the degrees of freedom of the Kruskal-Wallis test statistic?

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 test will involve _____ degrees of freedom.

SCENARIO 12-16 As part of an evaluation program,a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles.She took 3 of each brand and determined their maximum downhill speeds.The results are presented in miles per hour in the table below. -Referring to Scenario 12-16,the calculation of the Kruskal-Wallis test statistic H involves ranking the observations.Construct a table containing these ranks.

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 rank given to the second observation in the "scratch-and-sniff" group is .

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 should be the null and alternative hypotheses of the test?

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 A and procedure C are different at a 0.05 level of significance.

Which of the following is a "robust" test procedure against the violation of distribution assumptions?