The following sample data reflect shipments received by a large firm from three

Question

The following sample data reflect shipments received by a large firm from three different vendors Use Table 3 Vendor Defective Acceptable 112 70 150 2 10 a. Choose the competing hypotheses to determine whether quality is associated with the source of the shipments Ho Quality and source of shipment (vendor) are dependent; HA: Quality and source of shipment (vendor) are independent. Ho: Quality and source of shipment (vendor) are independent; HA: Quality and source of shipment (vendor) are dependent b-1. Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and your final answer to 2 decimal places.) df b-2. Specify the decision rule at a 1% significance level. (Round your answer to 3 decimal places.) Reject Ho if Xd> b-3. What is your conclusion? 0 Reject Ho; quality and source of shipment are dependent O Do not reject Ho; quality and source of shipment are not dependent. O Reject Ho; quality and source of shipment are not dependent O Do not reject Ho; quality and source of shipment are dependent. c. Should the firm be concerned about the source of the shipments? O Yes

Explanation / Answer

a. Option (ii) is correct as

H0:Quality and source of shipment is independent

Ha : Quality and source of shipment is dependent.

b. Here first we will calculate total items produced so that will helps us to calculate the proportion of defective items and that will helps us to calculate the expected defective items.

Total items produced is = 378

deffective items = 46

so Proportion of defective items = 46/378 = 0.1217

So expected number of defective items for :

Vendor 1 = (14 + 112) * 0.1217 = 126 * 0.1217 = 15.33

Vendor 2 = (10 + 70) * 0.1217 = 80 * 0.1217 = 9.74

Vendor 3 = (22 + 150) * 0.1217 = 172 * 0.1217 = 20.93

Same is for acceptable quantity.

The expected table is

so chi - square calculation table where X2  = (o - E)2/E

so X2= 0.2023= 0.20

b - 2 at alpha = 0.01, dF = 3-1 = 2

X2cr= 9.21

b-3

Dont reject the null hypothesis . and conclude that Quality and source of shipment is independent . Option 2 is correct.

c No, the company should not be concerned about source of shipments.

Vendor Defective Acceptable total 1 14 112 126 2 10 70 80 3 22 150 172 Sum 46 332 378

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