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 110 boxes that had been tampered with and ascertained that, for 65 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 30 other boxes, employees had stolen the goods, and for the remaining 15 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 0.01 significance level. (Round your answers to 3 decimal places.)

  

The chief of security for Mall of the Dakotas was directed to study the problem of missing goods. He selected a sample of 110 boxes that had been tampered with and ascertained that, for 65 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 30 other boxes, employees had stolen the goods, and for the remaining 15 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 0.01 significance level. (Round your answers to 3 decimal places.)

Explanation / Answer

here as degree of freedom =2 for which at 0.01 level reject Ho if X2 >9.2103

from above X2 =7.7273

observed Expected Chi square P O E=total*p =(O-E)^2/E 0.50 65 55.00 1.82 0.25 30 27.50 0.23 0.25 15 27.50 5.68 110 110 7.73

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