Exam 12: Chi-Square Tests and Nonparametric Tests

TABLE 12-15 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. Package Scratch 52 37 68 43 43 53 48 39 47 -Referring to Table 12-15, the rank given to the last observation in the "scratch-and-sniff" group is _____.

TABLE 12-14 A filling machine at a local soft drinks company is calibrated to fill the cans at an average amount of 12 fluid ounces and a standard deviation of 0.5 ounces. The company wants to test whether the standard deviation of the amount filled by the machine is indeed 0.5 ounces. A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces. -Referring to Table 12-14, the decision is to reject the null hypothesis when using a 10% level of significance.

TABLE 12-3 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. 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 5 memory locations differ. -Referring to Table 12-3, the degrees of freedom of the test statistic is

TABLE 12-9 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 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 Table 12-9, there is sufficient evidence to conclude that the proportions between procedure A and procedure B are different at a 0.05 level of significance.

TABLE 12-17 The director of the MBA program of a state university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good. Given below is the result from 215 students' view of the program before and after the orientation. After the Orientation Before theOrientation Good NotGood Total Good 93 37 130 Not Good 71 14 85 Total 164 51 215 -Referring to Table 12-17, the director should reject the null hypothesis using a 1% level of significance.

TABLE 12-9 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 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 Table 12-9, the critical value of the test is ______.

TABLE 12-20 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 Table 12-20, 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?

TABLE 12-19 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomized block design, the results are presented in the table that follows. Fields Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 Below is the Minitab output of the Friedman rank test: Friedman Test: Yield versus Varieties, Fields Friedman test for Yield by Varieties blocked by Fields $\mathrm { s } =$$10.00$ $\quad \mathrm { DF } = 2 \quad \mathrm { P } = 0.007$ Est Sum of Varieties Median Smith 5 13.500 5.0 Trevor 5 15.667 10.0 Walsh 5 18.533 15.0 Grand median = 15.900 -Referring to Table 12-19, the decision made at a 0.01 level of significance on the Friedman rank test for the difference in medians implies that the 3 medians are not all the same.

TABLE 12-1 A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and 1() seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below. Hispanic Non- Hispanic Seat belts worn 31 148 Seat belts not worn 283 330 -Referring to Table 12-1, at 5% level of significance, the critical value of the test statistic is

TABLE 12-13 According to an article in Marketing News, fewer checks 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 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. Year Check Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 325 375 -Referring to Table 12-13, what is the critical value?

To test whether one proportion is higher than the other in two related sample, you can use the Marascuilo procedure.

$\text { TABLE 12-14 }$ A filling machine at a local soft drinks company is calibrated to fill the cans at an average amount of 12 fluid ounces and a standard deviation of 0.5 ounces. The company wants to test whether the standard deviation of the amount filled by the machine is indeed 0.5 ounces. A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces. -Referring to Table 12-14, in order to perform the test, we need to assume that the amount filled by the machine has a normal distribution.

TABLE 12-18 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 Table 12-18, the calculated value of the Kruskal-Wallis test statistic H is______

TABLE 12-14 A filling machine at a local soft drinks company is calibrated to fill the cans at an average amount of 12 fluid ounces and a standard deviation of 0.5 ounces. The company wants to test whether the standard deviation of the amount filled by the machine is indeed 0.5 ounces. A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces. -Referring to Table 12-14, the p-value of the test is somewhere in between 5% and 10%.

TABLE 12-9 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 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 Table 12-9, the decision made suggests that the 4 procedures all have different proportions of clear operations.

TABLE 12-13 According to an article in Marketing News, fewer checks 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 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. Year Check Written Year 1 Year 2 par 3 Yes 225 175 125 No 275 325 375 -Referring to Table 12-13, what are the degrees of freedom of the test statistic?

TABLE 12-20 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 Table 12-20, what are the values of the absolute difference and the critical range for the Marascuilo procedure to test for the difference in proportions between Hong Kong and Paris using a 0.05 level of significance?

TABLE 12-3 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. 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 5 memory locations differ. -Referring to Table 12-3, the critical value of the test statistic at 1% level of significance is

TABLE 12-6 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 Table 12-6, which hypotheses should the dean use?

TABLE 12-2 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 notidentify 109 89 -The Kruskal-Wallis Rank Test for differences in more than two medians is a nonparametric alternative to