please solve by hand, do not use technology Thank you very much One of your prod

Question

please solve by hand, do not use technology

Thank you very much

One of your production lines has been demonstrating some inconsistent performance. Your colleagues in quality control sent you some data that indicated that in a simple random sample of 51 products, the variance of one of the product dimensions was found to be 16.7, which is outside of company parameters. You work with your group to identify several problem areas and implement corrective actions to address those errors. Subsequently, your quality group sends you the latest production results where it was found that in a sample of41 products, the variance had been reduced to 15.0. The variance has been reduced, but have you really fixed the problem?

Explanation / Answer

The sample variance has reduced from 16.7 to 15.

If this has statistically reduced needs to be checked, that is is var2 < var1 or not

If the problem is really fixed or not depends on the company parameters of the variance. If the acceptable variance for the company is say 15.5 then we need to check if var2<15.5 or not.

Hence the null and alternate hypothesis would be:

H0 : var2 = company standard

H1 : var2<company standard

If the null hypothesis is rejected then we can say that the variance is within limits

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