Exam 12: Chi-Square Tests and Nonparametric Tests

TABLE 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 Table 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.

The Kruskal-Wallis test is an extension of which of the following for two independent samples?

TABLE 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 Table 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.

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

TABLE 12-19 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 Table 12-19, the calculation of the Kruskal-Wallis test statistic H involves ranking the observations. Construct a table containing these ranks.

TABLE 12-18 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 Table 12-18, what should be the null and alternative hypotheses of the test?

TABLE 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 Table 12-9, at 5% level of significance, the critical value of the test statistic is

TABLE 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 Table 12-6, the null hypothesis cannot be rejected.

TABLE 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 Table 12-7, the decision made suggests that the 3 cities all have different proportions of hotels that correctly post minibar charges.

TABLE 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 Table 12-4, the calculated value of the test statistic is

TABLE 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 Table 12-3, the expected cell frequency in the Female/Non-Local cell is ________.

TABLE 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 Table 12-6, what is the expected number of shoppers who pay by check in year 1 if there is no difference in the proportion of shoppers who pay by check among the three years?

A test for the difference between two proportions can be performed using the chi-square distribution.

TABLE 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 Table 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 New York and Paris using a 0.05 level of significance?

TABLE 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 Table 12-10, find the rejection region necessary for testing at the 0.05 level of significance whether there is a relationship between defect rate and years of experience.

TABLE 12-8 A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles in San Diego County depends on ethnic status. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) 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 Table 12-8, at 5% level of significance, the critical value of the test statistic is

TABLE 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 π₁ and π₂ 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 Table 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?

TABLE 12-17 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 Table 12-17, the rank given to the last observation in the "scratch-and-sniff" group is ________.

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.

TABLE 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 Table 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."