Question

The following sample data reflect shipments received by a large firm from three different vendors and the quality of those shipments. (You may find it useful to reference the appropriate table: chi-square table or F table)

Vendor	Defective	Acceptable
1	28		126
2	12		78
3	33		246

a. Select the competing hypotheses to determine whether quality is associated with the source of the shipments.

• H₀: Quality and source of shipment (vendor) are independent.; H_A: Quality and source of shipment (vendor) are dependent.

• H₀: Quality and source of shipment (vendor) are dependent.; H_A: Quality and source of shipment (vendor) are independent.

b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

FIND THE TEST STATISTIC.

Answer 1

a)

H0: Quality and source of shipment (vendor) are independent.; HA: Quality and source of shipment (vendor) are dependent.

b)

Observed Frequencies
	Shipment Quality
Vendor	Defective	Acceptable	Total
1	28	126	154
2	12	78	90
3	33	246	279
Total	73	450	523

Expected Frequencies
	Shipment Quality
Vendor	Defective	Acceptable	Total
1	21.49522	132.5048	154
2	12.56214	77.43786	90
3	38.94264	240.0574	279
Total	73	450	523

fo-fe
6.50478	-6.50478
-0.56214	0.562141
-5.94264	5.942639

(fo-fe)^2/fe
1.968445	0.319326
0.025155	0.004081
0.906845	0.14711

Chi square = sum(Oi-Ei)^2/Ei
Chi square = 3.371

df = (r-1)*(c-1) = (3-1)*(2-1) = 2*1 = 2

critical value, =CHISQ.INV.RT(0.05,2) = 5.99

Since chisq < critical value, i fail to reject Ho and conclude that Quality and source of shipment (vendor) are independent.