Exam 12: Chi-Square Tests and Nonparametric Tests

The McNemar test is approximately distributed as a Student's t.

TABLE 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 Table 12-13,how many children in the survey spend no more than 6 hours watching TV and are more than 10 lbs.underweight?

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

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 form of the alternative hypothesis?

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,if the firm wanted to test whether this proportion has changed from the previous study,which represents the relevant hypotheses?

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,what is the expected number of employees with 1 to 4 years of training time and a high defect rate?

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. -In testing the difference between two proportions using the normal distribution,we may use either a one-tail Chi-square test or two-tail Z test.

TABLE 12-15 The director of the MBA program of a state university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good.Given below is the result from 215 students' view of the program before and after the orientation. -Referring to Table 12-15,which test should she use?

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,there is sufficient evidence to conclude that

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

When using the X² tests for independence,you should be aware that expected frequencies that are too small will lead to a large Type I error.

TABLE 12-16 A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces. -Referring to Table 12-16,the decision is to reject the null hypothesis when using a 10% level of significance.

TABLE 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 Table 12-2,the same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.

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 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?

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 are the degrees of freedom of the test statistic?

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.

In testing a hypothesis using the X² test,the theoretical frequencies are based on the

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

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.

To test whether one proportion is higher than the other in two related samples,you can use the McNemar test.