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STAT 420
Fall 2007
Homework #1
(due Friday, August 31, by 3:00 p.m.)
1.
We would like to test the effect of drugs 1 and 2 on a physiological measure X.
Consider the model:
X
1
1
, X
1
2
, … , X
1
n
are
i.i.d. N
(
μ
1
,
σ
2
)
X
2
1
, X
2
2
, … , X
2
n
are
i.i.d. N
(
μ
2
,
σ
2
)
Assume that
μ
1
= 6,
μ
2
= 5,
σ
2
= 4.
a)
i)
Find P
(
3 < X
1
1
< 9
).
ii)
Find
ε
so that P
(

X
1
1
– 6
 <
ε
) = 0.95.
b)
Let
1
X =
=
n
i
i
n
1
1
X
1
.
i)
Suppose
n
= 25. Find P
(
5 <
1
X < 7
).
ii)
Suppose
n
= 25. Find
ε
so that P
(

1
X – 6
 <
ε
) = 0.95.
iii)
Find the smallest value of
n
so that P
(

1
X – 6
 < 0.1
) > 0.95.
c)
Let
2
X
=
=
n
i
i
n
1
2
X
1
, D =
1
X –
2
X
. Suppose
n
= 25. Find P
(
0 < D < 2
).
2.
The salary of junior executives in a large retailing firm is normally distributed with
standard deviation
σ
= $1,500. If a random sample of 25 junior executives yields
an average salary of $16,400, what is the 95% confidence interval for
μ
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This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.
 Spring '07
 STEPANOV

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