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A manufacturer of an electrical component claims to have made changes in their manufacturing process to improve the quality of the component. Previously the component had a nonconforming rate of 10%. The supplier would like to provide you with 8 units for destructive testing to demonstrate that the nonconforming rate is now below 10%.
(a) If the nonconforming rate has dropped to say 8%, what is the proba bility that you would see no non-conforming items in a sample of size 8?
(b) If the non-conforming rate has increased to say 12% what is the prob ability that you would see no non-conforming items in a sample of size 8?
(c) How large of a sample would you need to estimate the non-conforming rate to within 5% with 95% confidence?
How would you determine which test would be appropriate to use? What characteristics of the problem would you use to determine which hypothesis test you should use? Explain your answer.
For an arch chosen at random in Arches National Park, use the preceding information to estimate the probability that the height of the arch poening is:
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