The operations manager of a company that manufactures shirts wants to determine

Question

The operations manager of a company that manufactures shirts wants to determine whether there are differences in the quality of workmanship among the three daily shifts. She randomly selects 600 recently made shirts and carefully inspects them. Each shirt is classified as either perfect or flawed, and the shift that produced it is also recorded. The accompanying table summarizes the number of shirts that fell into each cell. Do these data provide sufficient evidence at the 10% significance level to infer that there are differences in quality among the three shifts?

Shirt Condition

Shift

1

2

3

Perfect

240

191

139

Flawed

10

9

11

Shirt Condition

Shift

1

2

3

Perfect

240

191

139

Flawed

10

9

11

Explanation / Answer

Ans:

Test statistic:

Calculated chi square=2.351

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

p-value=CHIDIST(2.351,2)=0.3087

As,p-value>0.1,we fail to reject null hypothesis.

Above data does not provide sufficient evidence at the 10% significance level to infer that there are differences in quality among the three shifts

Expected(E) 1 2 3 Total perfect 240 191 139 570 flawed 10 9 11 30 Total 250 200 150 600 Observed(O) 1 2 3 Total perfect 237.5 190 142.5 570 flawed 12.5 10 7.5 30 Total 250 200 150 600 (O-E)^2/E 1 2 3 perfect 0.026 0.005 0.086 flawed 0.500 0.100 1.633 Total chi square=2.351

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