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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.COM. DEGREE EXAMINATION – COMMERCE
THIRD SEMESTER – November 2008
ST 3202/ST3200/4202 – ADVANCED STATISTICAL METHODS
Date : 13-11-08 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION A (10 X 2 = 20 marks)
Answer ALL questions.
- Explain the terms of attributes.
- What are the differences between quota sampling and stratified sampling?
- state the Axioms of the probability
- Define conditional probability.
- Define Binomial and poisson distribution.
- Distinguish between null and alternative hypothesis
- State central limit theorem
- Explain the term standard error.
- Explain the various types of control chart
- Costruct the ANOVA table of two-way classification
SECTION B (5 X 8 = 40 Marks)
Answer any FIVE questions
- 800 candidates of both sex appeared at an examination. The boys out numbered the girls by 15 %
of the total. The number of candidates who passéd exceed the number failed by 480. Equal
number of boys and girls failed in the examination. Prepare a 2×2 table and find the coefficient
of association and Comment.
- A can solve a problem of statistics in 4 out of 5 chances and B can do it in 2 out of 3 chances
If both A and B try the problem. Find the probability that the problem will be solved.
- If 3% of the electric bulbs manufactured by a company are defective, find the probability that in a
Sample of 100 bulbs exactly five bulbs are defective ( e -3 = 0.0498)
- A random sample of 200 tins of coconut oil gave an average weight of 4.95 kgs with a standard
Deviation of 0.21kg. Do we accept the hypothesis of net weight 5kg per tin at 1% level.
- In a survey of 200 boys, of which 75 intelligent, 40 had skilled fathers while 85 of the
Unintelligent boys has unskilled fathers. Do these figures support the hypothesis that
Skilled fathers have intelligent boys. Use x2 –test of 5 % level.
- Distinguish between np-chart and c- chart
- You are given below the values of sample mean (X) and the range (R) for ten samples of size 5
Each. Draw mean and range charts and comment on the state of control of the process.
Sample No: 1 2 3 4 5 6 7 8 9 10
X: 43 49 37 44 45 37 51 46 43 47
R: 5 6 5 7 7 4 8 6 4 6
You may use the following control chart constraint for n = 5, A2 = 0.58, D3 = 0 , D4 = 2.11
- State and prove Bolle’s inequality
SECTION C (2 X 20 = 40 Marks)
Answer any TWO questions
- (a) Given (ABC) = 137; (αBC) = 261; (ABC) = 313; (Aβr) = 284; (Abr) = 417; (αBr) = 420;
(αbC) = 490; (αbr) = 508; Find the frequencies (AB), (A) and N.
(b) Explain the procedure generally followed in testing of hypothesis.
- (a) There are 3 boxes containing respectively 1 White,2 Red, 3 block; 2 white,3 red, 1 black ball;
3 white , 1 red and 2 black ball. A box is chosen at random and from it two balls are drawn
At random. The two balls are 1 red and 1 white. What is the probability that they come from
(i) The first box (ii) second box (iii) third box.
(b) If 10% of the screws produced by an automatic machines are defectives, find the probability
That of 20 screws selected at random there are (i) exactly two defectives
(ii)at the most three defectives (iii) at least two defectives.
21.(a) The lives of 12 cars manufactured by two companies A and B are given below in years
| X | 14 | 15 | 18 | 12 | 18 | 17 | 19 | 21 | 19 | 16 | 12 | 11 |
| Y | 21 | 18 | 14 | 22 | 23 | 19 | 20 | 16 | 16 | 13 | 20 | 14 |
Which company will you choose to purchase a car? Give reason. Test at 5% level of significance.
(b) The data given below relate to two random samples of employees from the different states
Mean Variance Size
State I 28 40 16
State II 19 42 25
Test the hypothesis that variance of the populations are equal.
- Prepare a Two- way ANOVA on the data given below.
Treatment I
| I | II | III | |
| A | 30 | 26 | 38 |
| B | 24 | 29 | 28 |
| C | 33 | 24 | 35 |
| D | 36 | 31 | 30 |
| E | 27 | 35 | 33 |
Treatment I I
Use the coding method, subtracting 30 from the given numbers.
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