Exam 12: Chi-Square and Nonparametric Tests

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

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 expected cell frequency for the Procedure A/Clear cell is .

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,if the null hypothesis of no connection between time spent watching TV and time spent reading story books is true,how many children watching less than 2 hours of TV and reading more than 2 hours of story books on average can we expect?

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,there is sufficient evidence to conclude that the proportions between procedure A and procedure B are different at a 0.05 level of significance.

A local real estate appraiser analyzed the sales prices of homes in 2 neighborhoods to the corresponding appraised values of the homes.The goal of the analysis was to compare the distribution of sale-to-appraised ratios from homes in the 2 neighborhoods.Random and independent samples were selected from the 2 neighborhoods from last year's homes sales,8 from each of the 2 neighborhoods.Identify the nonparametric method that would be used to analyze the data.

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 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?

SCENARIO 12-8 A study was conducted to determine whether the use of seat belts in motor vehicles depends on the educational status of the parents.A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained,and each child was classified according to (1)parents' educational status (College Degree or Non-College Degree)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 Scenario 12-8,at 5% level of significance,there is sufficient evidence to conclude that

The procedure for the Wilcoxon rank sum test requires that you rank each group separately rather than together.

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 12-15 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 Scenario 12-15,what is the value of the Wilcoxon rank sum test statistic T₁ ?

SCENARIO 12-15 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 Scenario 12-15,what is the p-value of the test statistic?

SCENARIO 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 Scenario 12-4,the calculated value of the test statistic is

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

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 critical value of the test is .

SCENARIO 12-17 Three new different models of compact SUVs have just arrived at the market.You are interested in comparing the gas mileage performance of all three models to see if they are the same.A partial computer output for twelve compact SUVs of each model is given below: You are told that the gas mileage population distributions for all three models are not normally distributed. -Referring to Scenario 12-17,what is your conclusion on the test using a 5% level of significance?

Which of the following procedures would you use to make pairwise comparisons of the absolute differences for the sample proportions in a 2xc contingency table.

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?

If the assumptions of the one-way ANOVA F test are not met,which of the following tests could be used?

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,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.

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,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?