Exam 12: Chi-Square and Nonparametric

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 Canada and China using a 0.05 level of significance?

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 value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions using ? = 0)10?

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 critical value of the test is ________.

Which of the following is a "robust" test procedure against the violation of distribution assumptions?

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 test will involve _________ degrees of freedom.

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 B are different at a 0.05 level of significance.

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, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses? a) $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } = 0$ versus $H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } \neq 0$ b) $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \neq 0$ versus $H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } = 0$ c) $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \leq 0$ versus $H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } > 0$ d) $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \geq 0$ versus $H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } < 0$

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, to use the chi-square critical value for the Kruskal-Wallis test, the sample size in each group has to be greater than _____.