The Oxnard Retailers Anti-Theft Alliance (ORATA)published a study that claimed the causes of disappearance of inventory in retail stores were 30 percent shoplifting,50 percent employee theft,and 20 percent faulty paperwork.The manager of the Melodic Kortholt Outlet performed an audit of the disappearance of 80 items and found the frequencies shown below.She would like to know if her store's experience follows the same pattern as other retailers. Using α = .05,the critical value you would use in determining whether the Melodic Kortholt Outlet's pattern differs from the published study is
A)7.815
B)5.991
C)1.960
D)1.645

Question

The Oxnard Retailers Anti-Theft Alliance (ORATA)published a study that claimed the causes of disappearance of inventory in retail stores were 30 percent shoplifting,50 percent employee theft,and 20 percent faulty paperwork.The manager of the Melodic Kortholt Outlet performed an audit of the disappearance of 80 items and found the frequencies shown below.She would like to know if her store's experience follows the same pattern as other retailers.  Using α = .05,the critical value you would use in determining whether the Melodic Kortholt Outlet's pattern differs from the published study is
A)7.815 
B)5.991 
C)1.960 
D)1.645

Quizplus · Accepted Answer

To determine whether the Melodic Kortholt Outlet's pattern differs from the published study, we need to conduct a chi-square goodness-of-fit test. The null hypothesis is that the observed frequencies match the expected frequencies based on the published study's percentages, and the alternative hypothesis is that they do not match. Since there are three categories, the degrees of freedom for the test is 2 (df = k - 1).

Using α = .05 and df = 2, the critical value for the chi-square test is 5.991, which corresponds to the 95th percentile of the chi-square distribution with 2 degrees of freedom. If the calculated chi-square statistic is greater than the critical value, we reject the null hypothesis and conclude that there is evidence that the observed frequencies differ from the expected frequencies.

Therefore, the best choice is B, 5.991, since it is the critical value for the chi-square test with α = .05 and df = 2.

The Oxnard Retailers Anti-Theft Alliance (ORATA)published a Study That Claimed