Exam 12: Chi-Square and Nonparametric

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 value of the test statistic?

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 correct conclusion?

SCENARIO 12-15 Two new different models of compact SUVs have just arrived at the market. You are interested in comparing the gas mileage performance of both models to see if they are the same. A partial computer output for twelve compact SUVs of model 1 and thirteen of model 2 is given below: You are told that the gas mileage population distributions for both models are not normally distributed. -Referring to Scenario 12-15, what is the p-value of the test statistic?

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 degrees of freedom of the test statistic are

SCENARIO 12-8 A study was conducted to determine whether the use of seat belts in motor vehicles depends on the educational status of the parents. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) parents' educational status (College Degree or Non-College Degree) 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. Non-College Degree College Degree Seat belts not worn 31 148 Seat belts worn 283 330 -Referring to Scenario 12-8, the calculated test statistic is

SCENARIO 12-9 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 Scenario 12-9, which test would be used to properly analyze the data in this experiment? 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 12-3 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 Scenario 12-3, the overall or mean proportion of local riders 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 conclusion on the test using a 5% level of significance?

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 expected cell frequency for the Paris/No cell 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 should be the null and alternative hypotheses of the test? a) $H _ { 0 } : M _ { 1 } = M _ { 2 } = M _ { 3 }$ vs. $H _ { 1 } : M _ { 1 } \neq M _ { 2 } \neq M _ { 3 }$ b) $H _ { 0 } : M _ { 1 } = M _ { 2 } = M _ { 3 }$ vs. $H _ { 1 } : M _ { 1 } \neq M _ { 2 } = M _ { 3 }$ c) $H _ { 0 } : M _ { 1 } = M _ { 2 } = M _ { 3 }$ vs. $H _ { 1 } : M _ { 1 } = M _ { 2 } \neq M _ { 3 }$ d) $H _ { 0 } : M _ { 1 } = M _ { 2 } = M _ { 3 }$ vs. $H _ { 1 } :$ Not all $M _ { j }$ are equal (where $j = 1,2,3$ )

If we use the chi-square method of analysis to test for the difference between proportions, we must assume that there are at least 5 observed frequencies in each cell of the contingency table.

SCENARIO 12-12 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 -Referring to Scenario 12-12, to test whether there is any relationship between average time spent watching TV and average time spent reading story books, the value of the measured test Statistic is

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, suppose the value of the test statistic was 30.00 (which is not the correct value) and the critical value at 1% level of significance was 10.00 (which is not the Correct value), which of the following conclusions would be correct?

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 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?

SCENARIO 12-15 Two new different models of compact SUVs have just arrived at the market. You are interested in comparing the gas mileage performance of both models to see if they are the same. A partial computer output for twelve compact SUVs of model 1 and thirteen of model 2 is given below: You are told that the gas mileage population distributions for both models are not normally distributed. -Referring to Scenario 12-15, what is the standard deviation of the Wilcoxon rank sum test statistic T1?

SCENARIO 12-9 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 Scenario 12-9, at 5% level of significance, the critical value of the test statistic is

SCENARIO 12-3 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 Scenario 12-3, the expected cell frequency in the Female/Non-Local cell is __________.

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 assumptions needed to perform the test are satisfied.

The chi-square test of independence requires that the expected frequency in each cell to be at least 5.

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 expected cell frequency for the Procedure A/Clear cell is __________.