Exam 12: Chi-Square and Nonparametric

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. Non-College Degree College Degree Seat belts not worn 31 148 Seat belts worn 283 330 -Referring to Scenario 12-8, at 5% level of significance, the critical value of the test statistic is

SCENARIO 12-18 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 72%, respectively. Random samples of size 150 are selected from each of the three countries. You want to test for evidence of a difference among the proportions across the three countries using the 0.05 level of significance. -Referring to Scenario 12-18, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between U.S. and China using a 0.05 level of significance?

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, 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 12-12 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, how many children in the survey spent less than 2 hours watching TV and more than 2 hours reading story books on average?

SCENARIO 12-1 A corporation randomly selects 150 salespeople and finds that $66 \%$ who have never taken a selfimprovement 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 $\pi _ { 1 }$ and $\pi _ { 2 }$ 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, 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?

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: Admitted Wait List Denied Total Urban 45 21 17 83 Rural 33 13 24 70 Suburban 34 12 39 85 Total 112 46 80 238 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 test will involve _________ degrees of freedom.

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. Hong Kong New York Paris Yes 86\% 76\% 78\% No 14\% 24\% 22\% 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 null hypothesis will be rejected.

SCENARIO 12-16 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. 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46 -Referring to Scenario 12-16, the calculation of the Kruskal-Wallis test statistic H involves obtaining the total of the ranks for each sample. These totals are ________, ________, ________, and ________.

SCENARIO 12-18 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 72%, respectively. Random samples of size 150 are selected from each of the three countries. You want to test for evidence of a difference among the proportions across the three countries using the 0.05 level of significance. -Referring to Scenario 12-18, the decision made suggests that the 3 countries do not all have the same proportion of consumers who planned to spend more on holiday shopping.

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. Years Since Training Period <1 Year 1-4 Years 5-9 Years Defect Rate: High 6 9 9 Average 9 19 23 Low 7 8 10 -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 $\alpha = 0.05$

In testing a hypothesis using the $\chi ^ { 2 }$ test, the theoretical frequencies are based on the

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 null hypothesis should 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 the mean of the Wilcoxon rank sum test statistic T1?

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. Years Since Training Period <1 Year 1-4 Years 5-9 Years Defect Rate: High 6 9 9 Average 9 19 23 Low 7 8 10 -Referring to Scenario 12-10, what is the expected number of employees with 1 to 4 years of training time and a high defect rate?

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.

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. Hong Kong New York Paris Yes 86\% 76\% 78\% No 14\% 24\% 22\% 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 New York are different at a 0.05 level of significance.

SCENARIO 12-18 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 72%, respectively. Random samples of size 150 are selected from each of the three countries. You want to test for evidence of a difference among the proportions across the three countries using the 0.05 level of significance. -Referring to Scenario 12-18, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between U.S. and Canada using a 0.05 level of significance?

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, how many children in the survey spent less than 2 hours watching TV and no more than 2 hours reading storybooks on average?

SCENARIO 12-18 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 72%, respectively. Random samples of size 150 are selected from each of the three countries. You want to test for evidence of a difference among the proportions across the three countries using the 0.05 level of significance. -Referring to Scenario 12-18, the null hypothesis will be rejected.

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. 1 2 3 4 5 Number of Transactions: 82 100 74 92 102 Number of Reported Errors 11 12 6 9 10 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 degrees of freedom of the test statistic is