Homework 4 (due Feb. 20)
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
standard deviation is known to be equal to 10psi.
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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 Spring '08
 Perevalov
 Statistics, Standard Deviation, Statistical hypothesis testing, tomers

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