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. $$\begin{array} { | l | c | c | c | }
\hline \text { Reason } & \text { Shoplifting } & \text { Employee Theft } & \text { Poor Paperwork } \
\hline \text { Frequency } & 32 & 38 & 10 \
\hline
\end{array}$$ Under the null hypothesis that her store follows the published pattern, the expected number of items that disappeared due to shoplifting is:
A)16.
B)40.
C)24.
D)27.

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. $$\begin{array} { | l | c | c | c | } 
\hline \text { Reason } & \text { Shoplifting } & \text { Employee Theft } & \text { Poor Paperwork } \
\hline \text { Frequency } & 32 & 38 & 10 \
\hline
\end{array}$$ Under the null hypothesis that her store follows the published pattern, the expected number of items that disappeared due to shoplifting is:
A)16.
B)40.
C)24.
D)27.

Quizplus · Accepted Answer

Under the null hypothesis, we can calculate the expected frequencies for each reason of disappearance using the percentages given by the ORATA study.

Expected frequency of shoplifting = 0.3 x 80 = 24
Expected frequency of employee theft = 0.5 x 80 = 40
Expected frequency of poor paperwork = 0.2 x 80 = 16

The null hypothesis states that the distribution of reasons for disappearance in the store follows the same pattern as other retailers. Therefore, the expected frequency of shoplifting for the store is 24.

Since the observed frequency of shoplifting is 32, we can perform a chi-squared goodness-of-fit test to determine if this difference is statistically significant. However, we cannot directly use the chi-squared test statistic to answer the question "what is the expected frequency of shoplifting?" Therefore, the answer is C) 24, which represents the expected frequency of shoplifting under the null hypothesis.

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