Question

The chief of security for Mall of the Dakotas was directed to study the problem of missing goods. He selected a sample of 200 boxes that had been tampered with and ascertained that, for 110 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 50 other boxes, employees had stolen the goods, and for the remaining 40 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 0.10 significance level. Họ: The proportions are as stated. H: The proportions are not as stated. State the decision rule using 0.10 significance level. (Round your answer to 3 decimal places.) Reject HO 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 as stated.

Answer 1

SOLUTION:

From given data,

We test this with chi-square goodness of fit test.

Null hypothesis : : True proportions in all 3 categories is equal to their claimed value. that is = 0.5 , = 0.25 , = 0.25

Alternative hypothesis : : Alternative one proportions is different from its claimed value.

Atleast one do not matched the claimed value.

Expected fraction(p)	Observed (O)	Expected (E = n*p)	(O-E)^2 /E
0.5	110	100	1
0.25	50	50	0
0.25	40	50	2
	O = n = 200		= (O-E)^2 /E = 3

Value of chi-square:

= ​​​​​​​ (O-E)^2 /E

= 1+0+2

= 3

Decision Rule :

Significance level = 0.1

Degree of freedom = df = k-1 = 3-1 = 2

Critical value = = 4.605

Decision Rule : Reject if > 4.605

Decision Regarding ?

Test statistic is not greater than critical value ,We fail to reject null hypothesis .At 10% level,there is NOT significance evidence that atleast one of the proportions differs from its claimed value.