The chief of security for Mall of the Dakotas was directed to study the problem

Question

The chief of security for Mall of the Dakotas was directed to study the problem of missing goods. He selected a sample of 100 boxes that had been tampered with and ascertained that, for 48 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 20 other boxes, employees had stolen the goods, and for the remaining 32 boxes he blamed poor inventory control. In his report to the mall management, can he say that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely? Use the 0.02 significance level

Explanation / Answer

here expected proportion of shoplifting =1/2

expected proportion of employee theft =1/4

expected proportion of inventory control =1/4

applying chi square goodness of fit on above:

here degree of freedom =categories-1 =3-1=2

for 2 degree of freedom and above test stat 3.04 ; p value =0.2187

as p value is higher then 0.02 significance level we can not reject that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control

observed Expected Chi square Reason Probability O E=total*p =(O-E)^2/E shoplifting 1/2 48.000 50.00 0.08 employee theft 1/4 20.000 25.00 1.00 inventory control 1/4 32.000 25.00 1.96 1 100 100 3.0400

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