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

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: 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.

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 1 to 4 years of training time and a high defect rate?

In a chi-square test for the difference between two proportions, p is the estimate of the population parameter π if the null hypothesis of no group differences were false.

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 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?

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 12-11 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 will be rejected.

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 decision made suggests that there is a difference between the proportion of males and females who ride local versus non-local routes.

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 New York and Paris are different at 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 decision made suggests that the 3 cities all have different proportions of hotels that correctly post minibar charges.

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 overall or mean proportion of local riders 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: 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 B using a 0.05 level of significance?

If we use the chi-square method of analysis to test for the difference between proportions, we must assume that there are at least 5 observed frequencies in each cell of the contingency table.

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 value of the test statistic is ________.

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 form of the alternative hypothesis?

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 12-13 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- year-olds 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, if there is no connection between weights and average number of hours spent watching TV, we should expect how many children to be spending 3-6 hours on average watching TV and are more than 10 lbs.underweight?

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 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: 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.

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. -Referring to Scenario 12-14, the calculated value of the test statistic is ________.