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. $$\begin{array} { | l | c | c | c | }
\hline \text { Reason } & \text { Shoplifting } & \text { Employee Theft } & \text { Poor Paperwork } \
\hline \text { Frequency } & 32 & 38 & 10 \
\hline
\end{array}$$ Using ? = .05, the critical value you would use in determining whether the Melodic Kortholt'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. $$\begin{array} { | l | c | c | c | } 
\hline \text { Reason } & \text { Shoplifting } & \text { Employee Theft } & \text { Poor Paperwork } \
\hline \text { Frequency } & 32 & 38 & 10 \
\hline
\end{array}$$ Using ? = .05, the critical value you would use in determining whether the Melodic Kortholt'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 if the Melodic Kortholt Outlet's pattern differs significantly from the published study, we need to use a chi-square goodness-of-fit test. The null hypothesis is that the observed frequencies (32, 38, and 10) match the expected frequencies based on the ORATA study (24, 40, and 16). The degrees of freedom for this test are 2 (number of categories - 1).

We can use a chi-square calculator or table to find the critical value for this test with α = .05 and df = 2. The critical value is 5.991.

If the calculated chi-square value is greater than the critical value, we reject the null hypothesis and conclude that the observed frequencies differ significantly from the expected frequencies. If the calculated chi-square value is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to say that the observed frequencies differ significantly from the expected frequencies.

Since the question only asks for the critical value, the answer is B) 5.991.

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