# hw4 - Homework 4(due Feb 21 1 A company claims that the...

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Homework 4 (due Feb. 21) 1. A company claims that the mean bursting strength of bottles it pro- duces is at least 250 psi. To test this claim a representative of a potential customer takes a sample of 20 bottles and conducts a bursting strength test. She obtains the mean bursting strength of 244.9 psi for the sample, while the sample standard deviation turns out to be equal to 9.5 psi. a) Assuming that the customer is an old one and tends to trust the manufacturer, formulate the appropriate hypothesis and test it at α = 0 . 01 significance level. Should the customer believe the claim and buy a batch of these bottles? (Hint: since the customer trusts the manufacturer, he will give it the “benefit of a doubt” and use the “ < ” alternative hypothesis, and will buy the bottles if H 0 is not rejected.) b) Formulate the appropriate hypothesis and test it at α = 0 . 01 signifi- cance level assuming that the customer is new and tends to be suspicious of the manufacturer’s claim. What the customer’s decision would be this time?

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