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Assignment 4 Suggested Solutions
The Hong Kong University of Science and Technology
ISMT 111 - Business statistics, Fall 2004
Lecture Section 2 (Dr. So)
Problem Sheet 4
Suggested Solutions
1.
(1.6706, 63294)
2.
(25.42, 36.58)
3.
(69.9141, 93.0859)
4.
(620.13, 8879.87). Since 0 does not included in the interval, the employee can say that
there is a real difference between them.
5.
(1789.38, 7410.62)
6.
(a) 0.9184
(b) Point estimate
p
ˆ
= 120 / 200 = 0.6
The point estimate is good because
i.
it is unbiased
ii.
it has small standard error, 0.0354
(c) Maximum error of estimation = 0.05816 OR 0.05698
(d) The number of additional consumers is at least = 3258 - 200 = 3058
7.
(-0.2016, 0.0016)
8.
min.
n
= 151
9.
(a) (0.5377, 0.6865)
(b) The interval has 95% chance that it covers the true proportion
p
1
.
(c)
Choose
p
1
= 0.5,
⇒
min.
n
1
is 385
(d)
(-0.0308, 0.1773)
(e)
Since zero lies within the 95% C.I. for
p
1
–
p
2
, we can
’
t say that the premiere of
“
The
Cosby Show
”
is more popular than the premiere of
“
The X-files
”
.
10. (a) (36.596,64.312)
(b) (21.624, 36.464)
(c) (5.652 , 37.168)
11. (a) (0.4517, 0.5083)
(b) The confidence level is 90.3%.
(c) The minimum n = 1689

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