The number of defective items produced in a week by each of 5 different producti

Question

The number of defective items produced in a week by each of 5 different production lines (called A, B, C, D, and E) is as follows:

This data will be used to test if the lines are of equal quality, i.e. H0:p1=p2=p3=p4=p5=0.2

Use this information to answer questions 6 to 8.

If the production lines are of equal quality, how many defective items would we expect to be produced by line C?

What is the value of the Chi-square statistic for this test?

The p-value for this test is 0.0096. What are the appropriate decision and conclusion at the 1% significance level? (Select one of more)

A. We reject the null hypothesis.

B We cannot reject the null hypothesis.

C. There is evidence that the production lines are not of equal quality.

D. There is not enough evidence to say that the production lines are not of equal quality.

A B C D E Total 15 27 31 19 11 103

Explanation / Answer

defective items expected from line C =103/5 =20.60

applying chi square goodness of fit test on above:

value of the Chi-square statistic for this test =13.359

as p value is less then 1% ; therefore

A. We reject the null hypothesis.

C. There is evidence that the production lines are not of equal quality.

observed Expected Chi square Type Probability O E=total*p =(O-E)^2/E A 0.200 15.000 20.60 1.52 B 0.200 27.000 20.60 1.99 C 0.200 31.000 20.60 5.25 D 0.200 19.000 20.60 0.12 E 0.200 11.000 20.60 4.47 1 103 103 13.3592

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