THE UNIVERSITY OF HONG KONG
07/08
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT0301 Elementary Statistical Methods
Assignment 6
(Do ALL. Problems for selfpractice. No need to hand in.)
1. A sample of 123 students is classiﬁed with respect to appearance and with respect
to academic performance. Three categories of appearance: attractive, ordinary and
unattractive, and four categories of academic performance: high, fair, low, and poor,
are used. If the experimental results are as follows, test the hypothesis that there is
no relationship between the two characteristics against the general alternative.
H
F
L
P
Total
A
5
10
11
14
40
O
14
16
16
12
58
U
10
7
4
4
25
Total
29
33
31
30
123
2. In a random sample of 150 registered voters with low incomes 105 are for a certain
piece of legislation while 45 are against it; in a random sample of 160 voters with
average incomes 96 are for the legislation while 64 are against it; and in a random
sample of 100 voters with high incomes 42 are for the legislation while 58 are against
it. Test, for each pair of classes, the null hypothesis that the proportion of voters
favouring the legislation is the same against an alternative that they are not. Use
two methods.
3. A merchant stocks a certain perishable item. He knows that on any given day he
will have a demand of 250, 350, or 450 for these items with probabilities 0.2, 0.4, and
0.4, respectively. He buys the items for $12.0 each and sells them for $20.0 each. If
any are left at the end of the day, they are scrapped. How many items, 250, 350, or
450, should the merchant stock so as to maximize his expected daily proﬁt? What
is the maximum expected proﬁt? (Construct a proﬁts table ﬁrst.)
4. Members of a gamblers’ club are classiﬁed according to whether they drink, or smoke,
or otherwise, as shown below: A member is randomly chosen from the club.
Group
Male (M)
Female (F)
Drinker (D)
30
20
Smoker (S)
19
5
Both (B)
8
0
Otherwise (O)
49
35
(a) Show that the events of this member being a drinker and being a smoker are
independent.
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 Spring '07
 Dr.
 Science, Probability, Null hypothesis, Probability theory, Randomness, true proportion

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