Homework #1
Spring 2008
(due Friday, January 25, by 4:00 p.m.)
1.
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
, the average
salary of all junior executives.
σ
= $1,500,
n
= 25,
X = $16,400.
n
z
2
X
α
±
95% confidence,
= 0.05,
z
0.025
= 1.960.
25
500
,
1
960
.
1
400
,
16
⋅
±
16,400
±
588
(
15,812
, 16,988
)
2.
Redo Problem
1
without
assuming that the population standard deviation is known.
You are given
s
= $1,575.
s = $1,575,
n
= 25,
X = $16,400.
( )
n
t
n
s
1
2
X

±
95% confidence,
= 0.05,
t
0.025
(
24
) = 2.064.
25
575
,
1
064
.
2
400
,
16
⋅
±
16,400
±
650.16
(
15,749.84
, 17,050.16
)
3.
A cereal packaging machine is supposed to turn out boxes that contain 20 oz of
cereal on the average. Past experience indicates that the standard deviation of the
content weights of the packages turned out by the machine is
σ
= 0.25 oz. We wish
to test
H
0
:
μ
= 20 vs.
H
a
:
μ
< 20. If a sample of
n
= 20 items has mean weight
x
=
–
1.79.