Exam 12: Chi-Square Tests

When we carry out a chi-square test of independence,the chi-square statistic is based on (rc - 1)degrees of freedom,where r and c denote,respectively,the number of rows and columns in the contingency table.

At a recent meeting of educational researchers,comparisons were made between the type of college freshmen attend and the numbers who drop out.A random sample of freshmen shows the following results: Calculate the chi-square statistic for this test of independence.

Which,if any,of the following statements about the chi-square test of independence is false?

The AAA Co.is interested in the level of satisfaction of their employees with the benefit package that they offer compared to their major competitors.A consultant hired to conduct the satisfaction survey told AAA Co.that the distribution of level of satisfaction at other companies is displayed below: A survey was conducted of 125 AAA employees with the following results: What are the expected values of the number of AAA employees at each satisfaction level assuming a similar distribution as the major competitors of AAA?

A human resource manager is interested in whether absences occur during the week with equal frequency.The manager took a random sample of 100 absences and created the following table: Calculate the expected absences for all 5 days.

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed and expected frequencies. It is desired to test whether these measurements came from a normal population.Calculate the value of the chi-square test statistic.

AAA Co.operates distribution centers in the Midwest.Three of their centers were recently audited to determine if they are in compliance with company standard billing procedures.According to the auditing firm,a billing had an equal probability of being from each of the three centers.A random sample of the audited billings had the following distribution: What is the expected value of the number of billings for each center if H₀ (equal probabilities)is true?

The HR manager of a major office supply chain is interested in determining whether employee educational level affects knowledge of their job.An exam was given to 120 employees.The results are below: Test the null hypothesis that score is independent of education level at α = .01.

A manufacturing company produces part A732 for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part A732 is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items.At a significance level of .05,the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used.What is the rejection point condition?

A U.S.-based Internet company offers an online proficiency course in basic accounting.Completing this online course satisfies the Fundamentals of Accounting course requirement in many MBA programs.In the first semester,315 students have enrolled in the course.The marketing research manager divided the country into seven regions of approximately equal population.The course enrollment values for each of the seven regions are given below.The management wants to know if there is equal interest in the course across all regions. How many degrees of freedom are associated with the chi-square test? Also,at α = .05,determine the rejection point condition of the chi-square statistic.

The following frequency table summarizes the ages of 60 shoppers at the local grocery store. The estimated mean is 36.25,and the estimated standard deviation is 13.57.It is desired to test whether these measurements came from a normal population.At a significance of .01,test H₀: the sample of 60 shoppers came from a normal population.

When we carry out a chi-square test of independence,in the alternative hypothesis we state that the two classifications are statistically independent.

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been sold in the past month are randomly selected and their selling prices are recorded.The statistician working on the project has stated that in order to perform various statistical tests,the data must be distributed according to a normal distribution.In order to determine whether the selling prices of homes included in the random sample are normally distributed,the statistician divides the data into 6 classes of equal size and records the number of observations in each class.She then performs a chi-square goodness-of-fit test for normal distribution.The results are summarized in the following table. At a significance level of .05,what is the appropriate rejection point condition?

The following frequency table summarizes the ages of 60 shoppers at the local grocery store. The estimated mean is 36.25,and the estimated standard deviation is 13.57.It is desired to test whether these measurements came from a normal population.What is the df for this chi-square test of normality?

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies. It is desired to test whether these measurements came from a normal population.Calculate the expected frequency for the interval 40-59.99.

A manufacturing company produces part A732 for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part A732 is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items.At a significance level of .05,we performed a chi-square test of independence to determine if the quality of the items produced appears to be independent of the production process.What are the degrees of freedom for the chi-square statistic?

The χ² goodness-of-fit test requires the nominative level of data.

In performing a chi-square goodness-of-fit test for a normal distribution,a researcher wants to make sure that all of the expected cell frequencies are at least five.The sample is divided into 7 intervals.The second through the sixth intervals all have expected cell frequencies of at least five.The first and the last intervals have expected cell frequencies of 1.5 each.After adjusting the number of intervals,the degrees of freedom for the chi-square statistic is ____.

A manufacturing company produces part A732 for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part A732 is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items. Chi-Square Contingency Table Test for Independence At a significance level of .10,the management wants to perform a hypothesis test to determine if the quality of the items produced appears to be independent of the production process used.Based on the results summarized in the MegaStat/Excel output provided in the table above,we:

At a recent meeting of educational researchers,comparisons were made between the type of college that freshmen attend and the numbers who drop out.A random sample of freshmen shows the following results: At a significance level of .05,determine the appropriate degrees of freedom and the rejection point condition for this test.