2.) Occasionally, warning flares of the type contained in most automobile emerge
ID: 3269707 • Letter: 2
Question
2.) Occasionally, warning flares of the type contained in most automobile emergency kits fail to ignite A consumer advocacy group wants to investigate a claim against a manufacturer of flares brought by a person who claims that the proportion of defective flares is much higher than the value of 0.1 claimed by the manufacturer. A large number of flares will be tested, and the results will be used to decide between HO: µ = 0.1 versus HA: µ > 0.1, where represents the true proportion of defective flares made by this manufacturer. If HO is rejected, charges of false advertising will be filed against the manufacturer.
a.) Explain why the alternative hypothesis was chosen to be HA: µ > 0.1.
b.) In this context, describe Type I and Type II Errors, and discuss the consequences of each.
Explanation / Answer
a) Here the alternative is right sided because the claim of the person is that the proportion of defectives is more than 0.1 and claim should be on the alternative hypothesis. (Ans).
b) P(Type I error) = P(Rej H0 | H0 is true). Thus in this case Type I error will occur if we conclude proportion of defectives is more than 0.1, when it actually not.
Consequence of Type I error in this case will be that the manufacturer probably has to withdraw the lot and send it for inspection. So from the manufacturer's point of view they will suffer huge loss.
P(Type II error) = P(Fail to reject H0 | H0 is false)
So Type II error will occur in this case when we conclude proportion of defectives is not more than 0.1, when actually it is.
Consequence of Type II error will be that the manufacturer don't need to withdraw the lot or send it for inspection. But people using the lot will suffer.
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