STAT 420
Fall 2008
Homework #1
(10 points)
(due Friday, September 5, by 3:00 p.m.)
From the textbook:
3.5
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 95percent 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,
α
= 0.05,
z
0.025
= 1.960.
25
500
,
1
960
.
1
400
,
16
⋅
±
16,400
±
588
(
15,812
,
16,988
)
3.12
Redo Problem 3.5
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

±
α
95% confidence,
α
= 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
)