The chief of security for the Mall of the Dakotas directed a study of theft. He selected a sample of 140 boxes that had been tampered with and ascertained that, for 75 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 45 boxes, employees had stolen the goods, and for the remaining 20 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. H0: The proportions are as stated
The chief of security for the Mall of the Dakotas directed a study of theft. He selected a sample of 140 boxes that had been tampered with and ascertained that, for 75 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 45 boxes, employees had stolen the goods, and for the remaining 20 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.
H0: The proportions are as stated. H1: The proportions are not as stated.
a. State the decision rule using 0.02 significance level. (Round your answer to 3 decimal places.)
b. Compute the value of chi-square. (Round your answer to 3 decimal places.)
c. What is your decision regarding H0?
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