Based on the past, it is known that 5% of bags of potato chipsmanufactured in a
ID: 2951173 • Letter: B
Question
Based on the past, it is known that 5% of bags of potato chipsmanufactured in a facility have defective seals that cause thechips to become stale after a short shelf life. Themanufacturer is thinking about replacing its current sealing systemwith a new system in order to reduce the percentage of defectiveseals. The new system was tested and, in a sample of 200bags, 6 with defective seals were found. Should the new system bepurchased? Deploy an appropriate procedure to answer to thisquestion.---
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Explanation / Answer
Based on thepast, it is known that 5% of bags of potato chips manufactured in a facility have defective seals that cause the chips to becomestale after a short shelf life. The manufacturer is thinking aboutreplacing its current sealing system with a new system in order to reduce the percentageof defective seals. The new system was tested and, in a sample of 200bags, 6 with defective seals were found. Should the new system be purchased? Deployan appropriate procedure to answer to this question. Let us hypothesize that thenew system has the same Failure Rate as the old system, that is, {F.R. = 5%}. In order for us to"reject" this hypothesis and conclude that the new system has abetter failure rate, we must show that the probability of getting the observed6 defective seals (with the hypothesized old F.R. = 5%) is verysmall. We could then state that the new Failure Rate was probablybetter than the old Failure Rate. We apply the Binomial ProbabilityDist to determine the probability of getting 6 or less defective seals withthe old Failure Rate of 5%: BinomialProb{6 Or Less Defective Out Of200 With Old F.R. = 5%} = 0.1237 (determined from probabilitytables) To reject the original hypothesis, we usually require aboveprobability value to be very small, generally less than (0.05). This iscalled the "Level of Significance", here equal to (0.05 = 5%). Unfortunately, the above value is much larger than (0.05). Thus, we can NOTreject the original hypothesis, and conclude the new system is notsignificantly better than the old system: {New system shouldNOT be purchased since it is not significantly better than the old systemat a Level of Significance of 5%.} .
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