Exam 12: Chi-Square Tests and Nonparametric Tests

TABLE 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 Table 12-13,how many children in the survey spend more than 6 hours watching TV and are more than 10 lbs.overweight?

TABLE 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 Table 12-7,the decision made suggests that the 3 cities all have different proportions of hotels that correctly post minibar charges.

To test whether one proportion is higher than the other in two related samples,you can use the Marascuilo procedure.

TABLE 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 Table 12-5,what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure A and procedure C using a 0.05 level of significance?

TABLE 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 Table 12-6,what is the form of the null hypothesis?

TABLE 12-16 A filling machine at a local soft drinks company is calibrated to fill the cans at a mean amount of 12 fluid ounces and a standard deviation of 0.5 ounces.The company wants to test whether the standard deviation of the amount filled by the machine is 0.5 ounces.A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces. -Referring to Table 12-16,what is the value of the test statistic?

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

TABLE 12-19 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 Table 12-19,the calculation of the Kruskal-Wallis test statistic H involves obtaining the total of the ranks for each sample.These totals are ________,________,________,and ________.

TABLE 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 Table 12-7,the value of the test statistic is ________.

The Kruskal-Wallis rank test for differences in more than two medians is a nonparametric alternative to

TABLE 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 Table 12-6,what is the critical value?

TABLE 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 Table 12-5,the decision made suggests that the 4 procedures do not all have the same proportion of clear operations.

TABLE 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 Table 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.

TABLE 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 Table 12-12,if the null hypothesis of no connection between time spent watching TV and time spent reading storybooks is true,how many children watching less than 2 hours of TV and reading no more than 2 hours of storybooks on average can we expect?

TABLE 12-1 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 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 α = 0.10?

TABLE 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 Table 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?

TABLE 12-1 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. -A test for whether one proportion is higher than the other can be performed using the chi-square distribution.

TABLE 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: He will use this table to do a chi-square test of independence with a level of significance of 0.01. -Referring to Table 12-11,the value of the test statistic is ________.

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.

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