(Use Excel) The quality department at an electronics company has noted that, his

Question

(Use Excel) The quality department at an electronics company has noted that, historically, 93% of the units of a specific product pass a test operation, 5% fail the test but are able to be repaired, and 2% fail the test and need to be scrapped. Due to recent process improvements, the quality department would like to confirm whether these rates are still valid. A recent sample of 500 parts revealed that 478 parts passed the test, 17 parts failed the test but were repairable, and 5 parts failed the test and were scrapped. Table 3.

a. Choose the appropriate alternative hypothesis for the test.

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

Test statistic            

c. Approximate the p-value.

d-1. At the 5% significance level, what is your conclusion?

(Click to select)RejectDo not reject H0. At the 5% significance level, we conclude that at least one of the proportions are different from 0.93, 0.05, and 0.02.

d-2. Would your conclusion change at the 5% significance level?

At least one of the pi (i = 1, 2, 3) differs from its hypothesized value. All pi (i = 1, 2, 3) values differ from its hypothesized value.

Explanation / Answer

Ans:

Chi square test for goodness of fit:

a)Altenative hypothesis:

Atleast one of the pi differs from its hypothized value.

b)

c)df=3-1=2

p-value=CHIDIST(5.423,2)=0.066

So,p-value lies between 0.05 and 0.1

d-1)As,p-value>0.05

Do not reject H0. We can not conclude that atleast one of the proportions are different from 0.93,0.05 and 0.02.

d-2At 10% significance level.

p-value <0.1

Reject H0. We can conclude that atleast one of the proportions are different from 0.93,0.05,and 0.02.

(Yes,conclusion change at 10% significance level)

Observed(O) Expected€ (O-E)^2/E pass 478 465 0.36344086 fail but repaired 17 25 2.56 fail but scrapped 5 10 2.5 Total 500 500 5.423

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