Class -- read the attached Chi-Square document as well as Chapter 15 from the te

Question

Class -- read the attached Chi-Square document as well as Chapter 15 from the text. The following is a problem that involves a Chi-Square Goodness-of-Fit test involving unequal frequencies. Show all 5 steps of the test -- give it a try!

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 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 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 0.02 level.

Explanation / Answer

we go for chi-square test for goodness of test and

ch-square=sum((O-E)2/E) with k-1 df, O-observed frequency and E-expected frequency

here

and

answer of first part

chi-square=sum((O-E)2/E)=2 with 1 df

critical chi-square(0.02,1)=5.41

since calculated chi-square 2 is less than critical chi-square(0.02,1)=5.41 so we

so we accept the to sayshoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control

answer of second part

chi-square=sum((O-E)2/E)=10 with 1 df

critical chi-square(0.02,1)=5.41

since calculated chi-square 10 is more than critical chi-square(0.02,1)=5.41 so we

so we donot accept that employee theft and poor inventory control are equally likely

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