Exam 12: Chi-Square and Nonparametric Tests

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 value of the test statistic is .

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 last observation in the "scratch-and-sniff" group is .

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 null hypothesis will be rejected.

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 null hypothesis will be rejected if 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 critical value of the test is .

Suppose there is interest in comparing the median response time for three independent groups learning a specific task.The appropriate nonparametric procedure is

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,what are the values of the absolute difference and the critical range for the Marascuilo procedure to test for the difference in proportions between Hong Kong and New York 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,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 2 and year 3 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,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 1 and year 2 using 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 same decision would be made with this test if the level of significance had been 0.05.

SCENARIO 12-8 A study was conducted to determine whether the use of seat belts in motor vehicles depends on the educational status of the parents.A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained,and each child was classified according to (1)parents' educational status (College Degree or Non-College Degree)and (2)seat belt usage (worn or not worn)during the accident.The number of children in each category is given in the table below. -Referring to Scenario 12-8,at 5% level of significance,the critical value of the test statistic is

SCENARIO 12-1 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self- improvement course would like such a course.The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course.The groups are assumed to be independent random samples.Let $\pi$ ₁ and $\pi$ ₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study,respectively. -Referring to Scenario 12-1,what is the critical value when testing whether the population proportions are different if = 0.10?

SCENARIO 12-8 A study was conducted to determine whether the use of seat belts in motor vehicles depends on the educational status of the parents.A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained,and each child was classified according to (1)parents' educational status (College Degree or Non-College Degree)and (2)seat belt usage (worn or not worn)during the accident.The number of children in each category is given in the table below. -Referring to Scenario 12-8,the calculated test statistic is

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 test will involve degree(s)of freedom.

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,what is the expected number of employees with less than 1 year of training time and a high defect rate?

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 test will involve _____ degrees of freedom.

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,suppose the value of the test statistic was 30.00 (which is the correct value),which of the following conclusions would be correct?

When the parametric assumption on the distribution is met,a parametric test is usually more powerful than a nonparametric test.

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 decision made suggests that the 3 cities do not all have the same proportion of hotels that correctly post minibar charges.

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 0.01 rather than 0.05.