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(MATH144)[2002](f)final~4660^_92983.pdf
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MATH 244 Applied Statistics

Final Examination December 18, 2002


Please read the following instructions carefully before you begin the examination.

1. Do not begin until you are told to do so.

2. Please place your student identity card on your desk for verification purposes.

3. There are 6 questions in this examination. You have to answer all the questions.

4. You will have 3 hours to complete the examination.

5. Show all your works on all questions. It is to your advantage (for receiving partial marks) to show intermediate steps in all required calculations. You should use at least 4 decimal places in all your intermediate calculations.



6. You are allowed to use two pieces of formula sheet (A4 size written on both sides). No books, notes or other reading materials are permitted. Statistics tables that you may need are provided.

7. If you feel you need to think a lot for a question, skip it and return to it later. Some of the easiest question for you might be at the very end. So, choose your own order of answering the questions.

8. Anyone who is caught cheating, helping someone cheat, or who is suspected of cheating, will receive zero mark on this examination. There will be no exception.

9. Do your best, and good luck!!!















1. (20 marks) An Arts Council investigated nine randomly selected companies on their spending on works of art and profits.
Company
A
B
C
D
E
F
G
H
I

Arts spending (X)
($1000)
0
0.5
1.2
1.4
5.1
9.7
20.6
24.1
27.4

Profit (Y)
($1,000,000)
- 0.3
1.6
8.4
- 4.0
10.3
6.8
17.1
32.1
18.0



(a)
Fit the regression line of Y on X.
(5 marks)





(b)
Construct the ANOVA table.
(5 marks)





(c)
It was found that company J had spent $9,000 on art works and company K had spent $7,500 on art works. For each of these two companies, predict its profit by a 90% prediction interval. Which company can make higher profit?
(6 marks)





(d)
The Arts Council claims that increasing the companys spending on works of art leads to increased profit. Comment on this statement based on the above data.
(4 marks)



2. (17 marks) A sample of 1000 voters, randomly selected from a large city, showed 560 in favour of candidate Jones and 440 in favour of another candidate Bob. Let and be the proportions of voters in the whole city who are in favour of Jones and Bob respectively.



(a)
Construct a 95% confidence interval for each of and .


(6 marks)





(b)
A student claims that there should be more voters supporting Jones than supporting Bob. In order to establish his statement, what hypotheses should he test? Write down the hypotheses in terms of and .


(3 marks)





(c)
Test your hypotheses in