The operations meager of?company that mamthctures tires wMts to deermine whether

Question

The operations meager of?company that mamthctures tires wMts to deermine whether there are any differences-the quality of workmanship among the three daily shifts. She ngdenly selects 490 tires and caretily inspects them Each tire is eiher clasified as perfet, saniujlactory or dejective, and the shit that produced t s also recorded. The wo categocical varisables of iaterest are shift and coodition of the dire produced. The data can be mmarized by the accompanying two-way table Perfect Satisfactory Defective Total Shift 1 Shi 267 Sheft 336 total 1 210 1 278 A) This sample has degree of freedom DF II shih and quality are independest te B) Accuate to 2 decimal places, the epected count in row clmn 1 is ccurate to 2 decinal places, the component valer in wI column I of the table i No

Explanation / Answer

Solution:

A. DF = 4

B. E1,1 = 98.57

C. Component 1,1 = 0.72

D. X^2 = 12.07

E. P-value = 0.0168

Since p-value is less than 0.02 significance level, we reject Ho.

Yes.

Using megastat, the output

Col 1   Col 2   Col 3   Total   Row 1 Observed   107 123 0 230 Expected   98.57 130.49 0.94 230.00 (O - E)² / E   0.72 0.43 0.94 2.09 Row 2 Observed   67 84 0 151 Expected   64.71 85.67 0.62 151.00 (O - E)² / E   0.08 0.03 0.62 0.73 Row 3 Observed   36 71 2 109 Expected   46.71 61.84 0.44 109.00 (O - E)² / E   2.46 1.36 5.44 9.25 Total Observed   210 278 2 490 Expected   210.00 278.00 2.00 490.00 (O - E)² / E   3.26 1.82 6.99 12.07 12.07 chi-square 4 df .0168 p-value

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