Exam 11: Chi-Square Tests

TABLE 11-1 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 π1 and π2 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 11-1, the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which of the following is most correct?

TABLE 11-11 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: He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Table 11-11, the null hypothesis will be rejected.

TABLE 11-4 A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors. The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ. -Referring to Table 11-4, at 1% level of significance,

TABLE 11-3 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 Table 11-3, the expected cell frequency in the Male/Local cell is ________.

TABLE 11-2 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 Table 11-2, the p-value of the test is ________.

TABLE 11-5 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 four 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 Table 11-5, the decision made suggests that the four procedures do not all have the same proportion of clear operations.

TABLE 11-7 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 Table 11-7, the null hypothesis will be rejected.

TABLE 11-5 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 four 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 Table 11-5, the test will involve ________ degrees of freedom.

TABLE 11-12 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 Table 11-12, 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 ________.

TABLE 11-7 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 Table 11-7, the decision made suggests that the three cities do not all have the same proportion of hotels that correctly post minibar charges.

TABLE 11-9 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 Table 11-9, which test would be used to properly analyze the data in this experiment?

TABLE 11-11 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: He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Table 11-11, the same decision would be made with this test if the level of significance had been 0.05.

TABLE 11-13 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 regard 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 Table 11-13, how many children in the survey spend more than 6 hours watching TV and are more than 10 lbs. overweight?

TABLE 11-2 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 Table 11-2 , the value of the test statistic is ________.

TABLE 11-3 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 Table 11-3, the overall or mean proportion of local riders is ________.

TABLE 11-5 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 four 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 Table 11-5, the overall or mean proportion of clear operations is ________.

TABLE 11-13 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 regard 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 Table 11-13, the test is always a one-tail test.

TABLE 11-7 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. -When using the χ² test for independence, you should be aware that expected frequencies that are too small will lead to a large Type I error.

TABLE 11-11 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: He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Table 11-11, the p-value of this test is greater than 0.01.

TABLE 11-6 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 Table 11-6, what is the p-value of the test statistic?