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,what can you conclude from your analysis?
A) The store's pattern is clearly significantly different from the published data.
B) The store's pattern is almost,but not quite,significantly different from the published data.
C) The store's pattern is very close to the published data.
D) We can form no conclusion because Cochran's Rule is violated.

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,what can you conclude from your analysis?
A) The store's pattern is clearly significantly different from the published data. 
B) The store's pattern is almost,but not quite,significantly different from the published data. 
C) The store's pattern is very close to the published data. 
D) We can form no conclusion because Cochran's Rule is violated.

Quizplus · Accepted Answer

We need to perform a chi-square goodness-of-fit test to compare the observed frequency distribution in the Melodic Kortholt Outlet store with the expected frequency distribution based on the ORATA study. The expected frequencies can be calculated by multiplying the total number of items (80) by the percentages given in the study. The degrees of freedom for the test are (k-1), where k is the number of categories. In this case, k=3, so df=2. The critical value for chi-square with df=2 and α=.05 is 5.99. Calculating the test statistic using the formula: chi-square = Σ ((fo-fe)^2 / fe) = 5.81. Since 5.81 < 5.99, we fail to reject the null hypothesis that the observed frequency distribution is not significantly different from the expected frequency distribution based on the ORATA study. Therefore, we can conclude that the store's pattern is almost, but not quite, significantly different from the published data.

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