Exam 15: Chi-Square Tests

Instruction 15-2 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 Instruction 15-2,the value of the test statistic is _______.

Instruction 15-6 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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records: | Procedure | A B C D Total Clear 27 41 21 7 96 Return 11 15 9 11 46 Total 38 56 30 18 142 They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance. -Referring to Instruction 15-6,there is sufficient evidence to conclude that the proportions between procedure B and procedure D are different at a 0.05 level of significance.

Instruction 15-5 A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of five memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the five memory locations, along with the number of reported errors. Memory Location 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 five memory locations differ. -Referring to Instruction 15-5,the calculated value of the test statistic is

Instruction 15-8 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\% 65\% 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 Instruction 15-8,the decision made suggests that the three cities all have different proportions of hotels that correctly post minibar charges.

Instruction 15-6 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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records: | Procedure | A B C D Total Clear 27 41 21 7 96 Return 11 15 9 11 46 Total 38 56 30 18 142 They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance. -Referring to Instruction 15-6,the decision made suggests that the four procedures all have different proportions of clear operations.

Instruction 15-11 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 < Year Years 5-9 Years High 6 9 9 Defect Rate: Average 9 19 23 Low 7 8 10 -Referring to Instruction 15-11,which test would you use to properly analyse the data in this experiment to determine whether there is a relationship between defect rate and years of experience?

Instruction 15-12 The director of admissions at a local university is interested in investigating if admissions status (admitted, waiting list, denied admission) 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 run a chi-square test of independence with a level of significance of 0.01. -Referring to Instruction 15-12,the decision made suggests that admissions status at the university is independent of the type of community in which an applicant resides.

Instruction 15-1 A large organization randomly selects 150 employees and finds that 66% who have never taken a professional-development course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 employees wanted a professional-development 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 professional-development course in the recent study and the past study, respectively. -Referring to Instruction 15-1,what is the critical value when testing whether population proportions are different if α = 0.10?

Instruction 15-7 According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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. Cheque Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 175 125 -Referring to Instruction 15-7,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 2 and year 3 using a 0.05 level of significance?

Instruction 15-9 A study published in the Australian Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic background. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to 1. ethnic background (English Speaking Background (ESor Non-English Speaking Background (NESB)) 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. NESB ESB Seat belts worn 31 148 Seat belts not worn 283 330 -Referring to Instruction 15-9,the calculated test statistic is

Instruction 15-7 According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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. Cheque Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 175 125 -Referring to Instruction 15-7,what is the form of the null hypothesis?

Instruction 15-1 A large organization randomly selects 150 employees and finds that 66% who have never taken a professional-development course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 employees wanted a professional-development 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 professional-development course in the recent study and the past study, respectively. -Referring to Instruction 15-1,the organization 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?

Instruction 15-5 A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of five memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the five memory locations, along with the number of reported errors. Memory Location 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 five memory locations differ. -Referring to Instruction 15-5,which test would you use to properly analyse the data in this experiment?

Instruction 15-7 According to an article in Marketing News, fewer cheques are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by cheque 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. Cheque Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 175 125 -Referring to Instruction 15-7,what are the degrees of freedom of the test statistic?

Instruction 15-10 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. Male Celebrity Female Celebrity Identified product 41 61 Could not identify 109 89 -Referring to Instruction 15-10,the calculated test statistic is

Instruction 15-4 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. | Average time spent reading story books | average time spent watching TV Less than 1 hour Between 1 and 2 hours More than 2 hours Less than 2 hours 90 85 130 More than 2 hours 655 32 8 -Referring to Instruction 15-4,how many children in the survey spent less than 2 hours watching TV and more than 2 hours reading story books on average?

If you use the chi-square method of analysis to test for the difference between proportions,you must assume that there are at least five observed frequencies in each cell of the contingency table.

Instruction 15-6 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 centre wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records: | Procedure | A B C D Total Clear 27 41 21 7 96 Return 11 15 9 11 46 Total 38 56 30 18 142 They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a 0.05 level of significance. -Referring to Instruction 15-6,the decision made suggests that the four procedures do not all have the same proportion of clear operations.

If you use the χ² method of analysis to test for the differences among four proportions,the degrees of freedom are equal to

Instruction 15-8 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\% 65\% 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 Instruction 15-8,the critical value of the test is _______.