Exam 12: Chi-Square and Nonparametric Tests

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: 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, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure C and procedure D using 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. -Referring to Scenario 12-6, the null hypothesis cannot be rejected.

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 null hypothesis should be rejected.

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: 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 __________.

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 form of the null hypothesis?

The Journal of Business Venturing reported on the activities of entrepreneurs during the organization creation process.As part of a designed study, a total of 71 entrepreneurs were interviewed and divided into 3 groups: those that were successful in founding a new firm (n₁ = 34), those still actively trying to establish a firm (n₂ = 21), and those who tried to start a new firm but eventually gave up (n₃ = 16).The total number of activities undertaken (e.g., developed a business plan, sought funding, looked for facilities)by each group over a specified time period during organization creation was measured.The objective is to compare the mean number of activities of the 3 groups of entrepreneurs.Because of concerns over necessary assumption of the parametric analysis, it was decided to use a nonparametric analysis.Identify the nonparametric method that would be used to analyze the data.

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. -Referring to Scenario 12-9, at 5% level of significance, the critical value of the test statistic 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. 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 12-5 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: 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 C and procedure D 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. -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 12-5 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: 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 overall or mean proportion of clear operations is __________.

Suppose there is interest in comparing the median response time for three independent groups learning a specific task.The appropriate nonparametric procedure 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, 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. 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 New York are different at a 0.05 level of significance.

A test for whether one proportion is higher than the other can be performed using the chi-square distribution.

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, 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 12-16 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. -Referring to Scenario 12-16, the decision rule for a level of significance of 0.05 using the Kruskal-Wallis test is to reject the null hypothesis if the test statistic H is ________ assuming that the sample sizes were large enough to use a chi-square approximation.

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, 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 12-3 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: 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 12-7 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. 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 New York and Paris using a 0.05 level of significance?