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 140 boxes that had been tampered with and ascertained that, for 60 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 50 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. Ho: The proportions are as stated. H: The proportions are not as stated State the decision rule using 0.02 significance level. (Round your answer to 3 decimal places.) Reject H0 if chi-square > Compute the value of chi-square. (Round your answer to 3 decimal places.) Chi-square value What is your decision regarding Ho? HO. There is evidence to conclude that the proportions are not as stated

Explanation / Answer

Oi indicates the observed frequency and Ei indicates the expected frequency. proportion of shoplifting is twice the proportion of stolen goods and poor inventory and both proportion of slolen goods and poor inventory are equal.

hence proportion of stolen goods is 0.5 and other two are 0.25 each

Ei = npi

2 = [ (Oi - Ei)2 / Ei ] = 8.5714

Here df = 3-1 = 2

For 0.02 significance, critical value of chi square is 7.8241 (=CHISQ.INV.RT(0.02,2) - excel function to find the critical value. one can use standard table)

Reject H0 if chi-square > 7.8241

Chi-squre value = 8.5714

Reject H0. There is significant evidence to conclude that the proportions are not as stated

Oi Ei (Oi-Ei)^2/Ei shoplifting 60 70 1.4286 Stolen goods 30 35 0.7143 Poor Inventory 50 35 6.4286 8.5714

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