Homework 3 (due Feb. 14)
1.
An industrial engineer is responsible for testing a big batch of ball
bearings whose mean diameter is supposed to be equal to 3.750 mm.
She
took a sample of size 50, and set the critical values (for the sample mean
¯
x
) for the test at 3.740 mm and 3.760 mm. The standard deviation for the
diameter is known to be equal to 0.03 mm.
a) What significance level is she using for the test?
b) What would the significance level become if she set the critical values
to 3.743 and 3.757 mm, respectively?
c) What should the critical values be for
α
= 0
.
05?
d) Would she reject the null hypothesis
H
0
:
μ
= 3
.
750 at
α
= 0
.
05 if the
sample mean were equal to 3.741 mm?
2. Consider the situation of problem 1. Assume that the significance level
is set at 0.05.
a) Find the probability of type II error if the true mean diameter is equal
to 3.755 mm.
b) What would the type II error probability be if the true mean diameter
were 3.760 mm?
3. Consider the situation from problem 1 again. Assume that the critical
values for ¯
x
are set to ensure that the significance level be equal to 0.05
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 Spring '08
 Perevalov
 Statistics, Standard Deviation, Statistical hypothesis testing, Type I and type II errors, Statistical power

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