Exam 12: Chi-Square and Nonparametric

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: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { 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 level of significance of 0.05. -Referring to Scenario 12-5, the decision made suggests that the 4 procedures do not all have the same proportion of clear operations.

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, the test is always a one-tail test.

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 12-14 A perfume manufacturer is trying to choose between 2 magazine advertising layouts. An expensive layout would include a small package of the perfume. A cheaper layout would include a "scratch- and-sniff" sample of the product. The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate. The manufacturer presents the more expensive layout to 4 groups and determines the approval rating for each group. He presents the "scratch-and-sniff" layout to 5 groups and again determines the approval rating of the perfume for each group. The data are given below. Use this to test the appropriate hypotheses with the Wilcoxon Rank Sum Test with a level of significance of 0.05. 52 37 68 43 43 53 48 39 47 -Referring to Scenario 12-14, the calculated 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, 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. 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, 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? a) $\chi ^ { 2 }$ test for independence b) $\chi ^ { 2 }$ test for differences among more than two proportions c) Wilcoxon rank sum test for independent populations d) Kruskal-Wallis rank test

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 New York and Paris are different at a 0.05 level of significance.

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: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { 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 level of significance of 0.05. -Referring to Scenario 12-5, the decision made suggests that the 4 procedures all have different proportions of clear operations.

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, the null hypothesis cannot be rejected.

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: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { 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 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 C 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, there is sufficient evidence to conclude that the proportions between U.S. and Canada 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: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { 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 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 D are different at a 0.05 level of significance.

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 p-value of the test statistic?

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, which of the following is the correct conclusion on the order of the proportions among the three countries?

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, what is the critical value when performing a chi-square test on whether the population proportions are different if α = 0.05? a) $\pm 1.645$ b) $\pm 1.96$ c) $3.841$ d) $2.706$

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 will be rejected if the test statistic 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: -Referring to Scenario 12-17, what is your decision on the test using a 5% level of significance?

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 alternative hypothesis of the Kruskal-Wallis test is that ________.

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?