ORIE 360/560 Fall 2007
Assignment 10
Due Tuesday, Nov. 27 at 2:00 pm
Problem 1.
Consider a normal (
μ, σ
2
) population distribution with the value of
σ
2
known.
(a) What is the confidence level for the interval ¯
x
±
2
.
81
σ/
√
n
?
(b) What is the confidence level for the interval ¯
x
±
1
.
44
σ/
√
n
?
(c) What value of
z
α/
2
gives a 99.7% confidence level in the confidence interval formula?
(d) How large a sample size (i.e., what value of
n
) is necessary for a 95% confidence level confidence interval
of width 1? Of width 1/2? Of width 2?
(e) What value of
n
is necessary for a confidence interval of width 1 at the 90% confidence level? At the
99% confidence level? At the 99.9% confidence level?
Problem 2.
Suppose you are a statistical consulatant for a large consulting firm. In your job, you have
to report a whole lot of 95% confidence intervals. In fact, during the month of August, you reported 1,000
such confidence intervals.
Let
Y
be the number of confidence intervals you reported in August which actually contained the true mean
for the particular problem you were working one.
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 Fall '07
 EHRLICHMAN
 Normal Distribution, Standard Deviation, Student's tdistribution, Confidence Level

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