# Need Help on Sample Size Question

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• #44651

Arthur
Participant

I need some help on solving this question.
Could someone explain and teach me how to get the answer?
Given that the minimum pull strength is1.1 lbf, there is an agreement whereby any test reading less or equal to 1.05 lbf will be read as 1.0 lbf and any test value greater than 1.05 lbf will be treated as 1.1 lbf. Before evaluation, the process engineer does not have knowledge on the actual process standard deviation, but does know that the pull strength usually ranges from 1.0 lbf to 1.9 lbf. What should be the evaluation sample size if the engineer is to conduct a 2-sample t-test with a “not equal to” alternative hypothesis, a 95% confidence level and 20% b risk. The comparative test will be conducted on batch 1 and batch 2.
a.   Both batch 1 and batch 2 will have a combined sample size of 112 unitsb.   Both batch 1 and batch 2 will have a respective sample size of 112 unitsc.   Both batch 1 and batch 2 will have a combined sample size of 143 unitsd.   Both batch 1 and batch 2 will have a respective sample size of 143 units

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#143545

Eric Maass
Participant

If you are using Minitab, you would go to:Stat / Power and Sample Size / 2 sample t
That would bring up a screen that would include a button called “Options” – you can click on that to select your “not equal to” alternative hypothesis and your 95% confidence level.
Back on the main 2-sample t test sample size screen, you would need to enter any two among:
– sample sizes- differences- power values
Your power value would be 100% – your beta risk, so 80%.
You could enter the 4 possible sample sizes among a b c and d, and see how much of a difference you could detect…but, at some point, you will need to estimate a standard deviation. The range of pull strength from 1.0 to 1.9 lb-f  could be used to obtain that estimate of the standard deviation – but you would have to make an assumption, like that the range represents +/- 3 standard deviations.
Best regards,Eric

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