LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

NO 14

B.Com. DEGREE EXAMINATION – COMMERCE

FOURTH SEMESTER – APRIL 2008

ST 4205 / 4200/3202 – ADVANCED STATISTICAL METHODS

 

 

 

Date : 24/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION A

Answer all questions.                                                                                      (10 x 2 = 20)

1. Check the consistency of the following data:

N = 100, (A) = 48, (AB) = 24, (β) = 35.

1. Define Partial association.
2. Consider an experiment of throwing a die once. Let A be the event of getting an odd number and B be the event of getting a prime number. Verify whether A and B are mutually exclusive and exhaustive.
3. Let X be a Poisson random variable satisfying P(X=2) = 2P(X=3). Find the mean and variance of X.
4. Let Z be a standard normal random variable. Find P(Z > 1.2) and P(0 < Z < 0.6).
5. What is meant by standard error?
6. Define Type I error and Type II error in hypothesis testing.
7. Find the missing values in the following ANOVA table:

Source             df        Sum of squares            Mean sum of squares

Treatments      4          118                              ?

Blocks             ?          201                              ?

Error                10        ?

Total                20        500

1. Mention the difference between variable and attribute control charts.
2. What are control limits?

 

SECTION B

Answer any FIVE questions.                                                                    (5 x 8 = 40)

1. a.) Define Yule’s coefficient of association.                                                                                 b.) A teaacher examined 280 students in Economics and Auditing and found that 160 failed in Economics, 140 failed in Auditing and 80 failed in both the subjects. Calculate Yule’s coefficient of association between failure in Economics and Auditing and interpret the result.
2. a.) A bag contains 10 white and 6 black balls. 4 balls are successively drawn out and not replaced. What is the probability that they are alternately of different colors?

b.) In a single throw of a die, what is the probability of obtaining a total of atleast 10?

1. Suppose 300 misprints are distributed randomly throughout a book of 500 pages. Find the probability that a given page contains a.) exactly 2 misprints  b.) no misprints and c.) 2 or more misprints.
2. Consider a population containing 5 values namely 12, 14, 10, 15, 12. Draw all possible random samples of size 2 from this population and obtain the sampling distribution of mean. Verify whether the sample mean is an unbiased estimator of the population mean.
3. Explain the procedure of testing the equality of proportions of two populations.
4. The number of units of a product sold in six shops before and after a promotional campaign are shown below:

Shops: A         B         C         D         E          F

Before campaign:  53        28        31        48        50        42

After campaign:  58        29        30        55        56        45

Can the campaign be judged to be a success? Test at 5% level.

1. Explain the various steps in performing a One – way Analysis of Variance.
2. 20 tape recorders were examined for quality control test. The number of defects for each tape recorder are given below:

2, 4, 3, 1, 1, 2, 5, 3, 6, 7, 3, 1, 4, 2, 3, 1, 6, 4, 1 and 1. Construct a suitable control chart and interpret it.

SECTION C

Answer any TWO questions.

1. a.) Given the following data, find frequencies of i.) the remaining positive classes and ii.) ultimate classes.

N = 1800, (A) = 850, (B) = 780, (C) = 326, (ABγ) = 200, (AβC) = 94,

(αBC) = 72 and (ABC) = 50.

b.) A manufacturing firm produces units of a product in four plants. Define event

A_i : a unit is produced in plant i, i = 1,2,3,4 and event B: a unit is defective. From

the past records of the proportions of defectives produced at each plant the

following conditional probabilities are set:

P(B|A₁) = 0.05, P(B|A₂) = 0.10, P(B|A₃) = 0.15 and P(B|A₄) = 0.02.

The first plant produces 30% of the units of the product, the second 25%, the third

40% and fourth 5%. A unit of the product made at one of these plants is tested

and found to be defective. What is the probability that the unit was produced either

in plant 1 or plant 3.                                                                                   (14+6)

1. a.) A fair coin is tossed four times. Let X denote the number of heads occurring. Find i.) the distribution function of X, ii.) expectation and variance of X.

b.) Suppose the weights of 2000 male students are normally distributed with mean 155 pounds and standard deviation 20 pounds. Find the number of students with weights: i.) less than 100 pounds  ii.) between 150 and 175 pounds

and iii.) more than 200 pounds.                                                            (12+8)

1. a.) Construct and R charts for the following data:

Sample:      1          2          3          4          5          6          7          8

X₁:      32        28        39        50        42        50        44        22

X₂:      37        32        52        42        45        29        52        35

X₃:      42        40        28        31        34        21        35        44

b.) The life time (in thousand hours) of electric bulbs based on a random sample of 10 from a large consignment gave the following data:

Unit:    1          2          3          4          5          6          7          8

Life time:    4.2       4.6       3.9       4.1       5.2       3.8       3.9       4.3

Unit:    9          10

Life time:    4.4       5.6

Test at 5% level, the hypothesis that the mean life time of bulbs in the entire

consignment is 4000 hours.                                                                          (12+8)

1. Three types of indoor lighting A₁, A₂ and A₃ were tried on three types of flowers B₁, B₂ and B₃. The average heights (in cm’s) after 12 weeks of growth are indicated in the following table:

Flowers

Lightning        B₁        B₂        B₃

A₁        16        24        19

A₂        15        25        18

A₃        21        31        15

Test at 5% level whether there is significant difference in growth due to lightning and due to

flower type.

 

 

 

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BA 31

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.         

                                  

1. Explain the terms of attributes.
2. What are the differences between quota sampling and stratified sampling?
3. state the Axioms of the probability
4. Define conditional probability.
5. Define Binomial and poisson distribution.
6. Distinguish between null and alternative hypothesis
7. State central limit theorem
8. Explain the term standard error.
9. Explain the various types of control chart
10. Costruct the ANOVA table of two-way classification

SECTION B                                              (5 X 8 = 40 Marks)

     Answer any FIVE questions

 

11. 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.

 

12. 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.

 

13. 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)

 

14. 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.

 

15. 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.

 

16. Distinguish between np-chart and c- chart

 

17. 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

 

18. State and prove Bolle’s inequality

 

 

SECTION   C                                   (2 X 20  =  40 Marks)

Answer any TWO questions

 

19. (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.

 

 

20. (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.

 

22. 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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