Exam 12: Chi-Square Tests and Nonparametric Tests

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."

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,for the cell with 1 to 4 years of training time and a high defect rate,what is the contribution to the overall X² statistic for the independence test?

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,the test is always a one-tail test.

In testing for differences between the median of two independent populations,the null hypothesis is

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,what are the lower and upper critical values of the test when allowing for 5% probability of committing a type I error?

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 is the value of the Wilcoxon rank sum test statistic T₁?

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,the test will involve ________ degrees of freedom.

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 12-18 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 is the value of the Z test statistic?

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 alternative hypothesis claims that "there is some connection between admission status at the college and the type of community in which an applicant resides."

TABLE 12-12 Parents complain that children read too few storybooks and watch too much television nowadays.A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks. -Referring to Table 12-12,suppose we want to constrain the probability of committing a Type I error to 5% when testing whether there is any relationship between average time spent watching TV and average time spent reading storybooks,the critical value will be

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 is the standard deviation of the Wilcoxon rank sum test statistic T₁?

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 is your decision on the test using a 5% level of significance?

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 will be rejected.

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 decision rule for a level of significance of 0.05 using the Kruskal-Wallis test is to reject the null hypothesis if the test statistic H is ________ assuming that the sample sizes were large enough to use a chi-square approximation.

The McNemar test is approximately distributed as a standardized normal random variable.

When testing for independence in a contingency table with 3 rows and 4 columns,there are ________ degrees of freedom.

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 sporting goods retailer decided to perform a Kruskal-Wallis test even though the sample size in each of the 4 groups is not larger than 5.The null hypothesis of the test is ________.

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,which test would be used to properly analyze the data in this experiment?

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,which test would be used to properly analyze the data in this experiment to determine whether there is a relationship between defect rate and years of experience?