Exam 12: Chi-Square Tests and Nonparametric Tests

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 the Orientation Good NotGood Total Good 93 37 130 Not Good 71 14 85 Total 164 51 215 -Referring to Table 12-17, what should be the director's conclusion?

TABLE 12-12 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 average number of hours spent watching TV and weights are independent at 1% level of significance. TV Hours Weights 0-3 3-6 6+ Total More than 10 lbs. Overweight 1 9 20 30 Within 10 lbs. of normal weight 20 15 15 50 More than 10 lbs. underweight 10 5 5 20 Total 31 29 40 100 -Referring to Table 12-12, which of the following statements is correct?

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, 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?

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 New York using a 0.05 level of significance?

In testing the difference between two proportions using the normal distribution, we may use either a one-tailed Chi-square test or two-tailed Z test.

The procedure for the Wilcoxon rank sum test requires that we rank each group separately rather than together.

Suppose there is interest in comparing the median response time for three independent groups learning a specific task. The appropriate nonparametric procedure is

A test for the difference between two proportions can be performed using the chi-square distribution.

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, there is not sufficient evidence to conclude that the proportions between year 1 and year 3 are different at 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. 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 N Median Ranks 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, what is the critical value of the Friedman rank test for the difference in the medians at a level of significance of 0.01?

The McNemar test is approximately distributed as a chi-square random variable.

TABLE 12-5 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 u₁ and u₂ 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 Table 12-5, what is the critical value when testing whether population proportions are different if α = 0.10?

TABLE 12-7 The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following: Male Female Total Local 27 44 71 Non- Local 33 25 58 Total 60 69 129 She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05. -Referring to Table 12-7, the null hypothesis will be rejected.

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. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Year }$ Check Written Year 1 Year 2 ear 3 Yes 225 175 125 No 275 325 375 -Referring to Table 12-13, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 1 and year 2 using a 0.05 level of significance?

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, what is the value of the test statistic?

TABLE 12-12 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 average number of hours spent watching TV and weights are independent at 1% level of significance. TV Hours Weights 0-3 3-6 6+ Total More than 10 lbs. Overweight 1 9 20 30 Within 10 lbs. of normal weight 20 15 15 50 More than 10 lbs. underweight 10 5 5 20 Total 31 29 40 100 -Referring to Table 12-12, the critical value of the test will be

TABLE 12-8 The director of transportation of a large company is interested in the usage of the company's van pool program. She surveyed 129 of her employees on the usage of the program before and after a campaign to convince her employees to use the service and obtained the following: $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Before }$ Use Do Not Use Total After Use 27 44 71 Do Not Use 33 25 58 Total 60 69 129 She will use this information to perform test using a level of significance of 0.05. -Referring to Table 12-8, the director now wants to know if the proportion of employees who use the service before the campaign and the proportion of employees who use the service after the campaign are the same. What should be her conclusion?

TABLE 12-11 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 2hours Less than 2 hours 90 85 130 More than 2 hours 655 32 8 -Referring to Table 12-11, 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

TABLE 12-16 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 both layouts to 5 groups and determines the approval rating from each group on both layouts. The data are given below. Use this to test whether the median difference in approval rating is different from zero in favor of the more expensive layout with a level of significance of 0.05. Package Scratch 52 37 68 43 43 53 48 39 56 47 -Referring to Table 12-16, which pair(s) of observations has a negative signed rank?

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 perfume manufacturer will