Exam 12: Chi-Square and Nonparametric Tests

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 are the degrees of freedom of the 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 decision made suggests that the 4 procedures all have different proportions of clear operations.

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,how many children in the survey spent less than 2 hours watching TV and no more than 2 hours reading storybooks on average?

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,how many children in the survey spend more than 6 hours watching TV and are more than 10 lbs.overweight?

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 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 decision made suggests that the 3 cities all have different proportions of hotels that correctly post minibar charges.

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,how many children in the survey spent less than 2 hours watching TV and more than 2 hours reading story books on average?

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 obtaining the total of the ranks for each sample.These totals are _____,_____,_____,and _____ .

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 decision made suggests that the 4 procedures do not all have the same proportion of clear operations.

In computing the expected cell frequencies for a chi-square test of independence,which of the following statements could be included in the correct procedure?

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 C using a 0.05 level of significance?

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 expected cell frequency for the Paris/No cell 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 critical value of the test 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,there is sufficient evidence to conclude that the proportions between Hong Kong and Paris are different at 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 3 using a 0.05 level of significance?

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 critical value of the test 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 calculated 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,the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study.Which of the following is most correct?

The squared difference between the observed and theoretical frequencies should be large if there is no significant difference between the proportions.

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 critical value of the test is .