Exam 11: Chi-Square Tests

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. Year Check Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 325 375 -Referring to Scenario 12-6, there is sufficient evidence to conclude that the proportions between year 2 and year 3 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. Year Check Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 325 375 -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 1 and year 2 using a 0.05 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, there is sufficient evidence to conclude that the proportions between Hong Kong and Paris are different at a 0.05 level of significance.

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, the degrees of freedom of the test statistic are

SCENARIO 12-11 The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table: Admitted Wait List Denied Total Urban 45 21 17 83 Rural 33 13 24 70 Suburban 34 12 39 85 Total 112 46 80 238 He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Scenario 12-11, the same decision would be made with this test if the level of significance had been 0.05.

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 Average time spent reading story books Average time spent watching TV Less than 1 hour Between 1 and 2 hours More than 2 hours Less than 2 hours 90 85 130 More than 2 hours 655 32 8 -Referring to Scenario 12-12, if the null hypothesis of no connection between time spent watching TV and time spent reading story books is true, how many children watching less than 2 hours of TV and reading no more than 2 hours of story books on average can we expect?

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. Year Check Written Year 1 Year 2 Year 3 Yes 225 175 125 No 275 325 375 -Referring to Scenario 12-6, what is the critical value?

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 null hypothesis will be rejected.

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. Weights TV Hours Total 0-3 3-6 6+ 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 Scenario 12-13, if there is no connection between weights and average number of hours spent watching TV, we should expect how many children to be spending no more than 6 hours on average watching TV and are more than 10 lbs.underweight?

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 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 decision made suggests that there is a difference between the proportion of males and females who ride local versus non-local routes.

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, which test would be used to properly analyze the data in this experiment?

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 p-value of the test 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. Weights TV Hours Total 0-3 3-6 6+ 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 Scenario 12-13, the test is always a one-tail 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, 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?

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 Hong Kong/Yes cell is.

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 decision made suggests that the 3 cities all have different proportions of hotels that correctly post minibar charges.

SCENARIO 12-11 The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table: Admitted Wait List Denied Total Urban 45 21 17 83 Rural 33 13 24 70 Suburban 34 12 39 85 Total 112 46 80 238 He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Scenario 12-11, the p-value of this test is greater than 0.01.

SCENARIO 12-11 The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table: Admitted Wait List Denied Total Urban 45 21 17 83 Rural 33 13 24 70 Suburban 34 12 39 85 Total 112 46 80 238 He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Scenario 12-11, the value of the test statistic is .

SCENARIO 12-11 The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides.He takes a sample of recent admissions decisions and forms the following table: Admitted Wait List Denied Total Urban 45 21 17 83 Rural 33 13 24 70 Suburban 34 12 39 85 Total 112 46 80 238 He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Scenario 12-11, the alternative hypothesis claims that "there is some connection between admission status at the college and the type of community in which an applicant resides."