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Anova -- chi square - "Mall of the Dakotas"

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The chief of security for the 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 60 boxes of the boxes, the missing pants, shoes and so on were attributed to shoplifting. For 30 of the boxes employees had stolen the goods, and the remaining 10 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 .02 level.

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Solution Summary

The solution is a detailed written solution of calculating the chi-square value using the equation and the chi-square tables.

Solution Preview

Known variables:

Sample size n = 100 boxes
r1 = 60, r2 = 30 and r3 = 10 (observations on missing pants/shoplifting, stolen goods, poor inventory control)

Now the observed values are converted in ratio as:
6 : 3 : 1

Expected value:
Ei = (6+ 3 + 1)/3 = 10/3 = 3.33

Chi-square table:

Oi Ei Oi - Ei (Oi - Ei)2 (Oi - Ei)2/ Ei
6 3.33 2.67 7.1289 ...

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