Exam 12: Chi-Square and Nonparametric Tests

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

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, the null hypothesis will be rejected.

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

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 B and procedure D using a 0.05 level of significance?

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 same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

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 Hong Kong and Paris are different at a 0.05 level of significance.

SCENARIO 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 Scenario 12-9, at 5% level of significance, the conclusion is that

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 1 and year 2 are different at a 0.05 level of significance.

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 p-value of this test is greater than 0.01.

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 claims that "there is no association between admission status at the college and the type of community in which an applicant resides."

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 B and procedure C are different at a 0.05 level of significance.

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, the critical value of the test 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- 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, which of the following statements is correct?

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 critical value of the test is ________.

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, a test was conducted to determine if a relationship exists between defect rate and years of experience.Which of the following p-values would indicate that defect rate and years of experience are dependent? Assume you are testing at = 0.05.

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 same decision would be made with this test if the level of significance had been 0.005.

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, what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions using = 0.10?

SCENARIO 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 Scenario 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 story books, the critical value will be