LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

YB 09

B.Com. DEGREE EXAMINATION – COMMERCE

THIRD SEMESTER – April 2009

ST 3202 / 3200 – ADVANCED STATISTICAL METHODS

 

 

 

Date & Time: 27/04/2009 / 9:00 – 12:00  Dept. No.                                                  Max. : 100 Marks

PART-A

Answer all the questions                                                                               ( 10 x 2 = 20)

1) Explain the difference between an attribute and a variable with examples.

2) Name the methods used to study the association of attributes.

3) A bag contains 8 white and 4 red balls. Five balls are drawn at random. What is the

probability that 2 of them are red and 3 are white?

4) Define probability of an event.

5) For a binomial distribution mean is 20 and variance is 16. Find n, p.

6) What is the standard error of the sample mean and the sample proportion?

7) What is significance level?

8) What are the control limits for a c- chart?

9) Write the 95% confidence interval for the sample mean when n is large.

10) State any two uses of chi-square distribution.

PART-B 

Answer any 5 questions                                                                         (  5 x 8 = 40 )

 

11) Find the association between literacy and unemployment from the following data.

            Total adults                             10,000

Literates                                  1290

Unemployed                           1390

Literate unemployed               820

Comment on the results.

12) One bag contains 4 white, 2 black and 3 blue balls. Another contains 3 white 5 black and 2 blue

balls. One ball is drawn from each bag.

Find the probability that   a) both are white

1. b) one is white and one is black
2. c) the sample should not have any blue balls.

13) A certain automatic machine produces one defective screw out of every 100 screws.

If the screws are packed in boxes of 300, what percentage of these boxes

would you expect to have

1. i) no defective screw?
2. ii) at least one defective screw

iii) not more than 2 defectives.

14) Explain the method of analysis of variance for one way classification.

15) Explain the theory behind control charts.

16) From the following data find out whether there is any relationship between sex and                preference of color for 200 samples.

Color                           males                           females

Red                             10                                40

White                          70                                30

Green                          30                                20

17) 15,000 students appeared for an examination. The mean marks obtained are 49 and the standard

deviation is 6. Assuming normal distribution, what proportion of students scored more

than 55 marks? If grade A is given to those who scored above 70, what proportion of students

will receive grade A?

18) Ten specimens of copper wires drawn from two large lots have the following breaking strengths

(in kgs) 578, 572, 570, 568, 512, 578, 570, 575, 569, 548.

Test whether the mean breaking strength of the lot may be taken to be 578 kg.

PART-C

Answer any 2 questions                                                                         ( 2 x 20 = 40 )

19) a) A survey of male children in 128 families each having 5 children gave the following data.

No of male children	0    1      2      3       4      5
No of families	9   17    26    39    22     12

Fit a binomial distribution to the data assuming p is not known.

 

1. b) In a bolt factory machines A, B, and C. produce respectively 25%, 35%, and 40%. Of the total of

their output 5, 4 and 2 percent are defective bolts. A bolt is drawn at random from the product

and is found to be defective. What is the probability that  it was manufactured by machines

A, B and C.?                                                                                                                   ( 10 + 10 )

20) a) You are working as a purchase manager for a company. The following

information has been supplied to two manufactures of electric bulbs.

	Company A	Company B
Mean life(hours)	1275	1248
SD	82	93
Sample size	100	100

Test whether there is any significant difference between the mean of  two products.

1. b) Before an increase in excise duty on tea 400 people out of 500 were found to be

tea drinkers. After an increase in the duty 400 persons were known to be tea drinkers

in another independent sample of 600 people. Test whether there is any

significant difference between the two cases?                                           ( 10 +10 )

 

21) a)100 children took three examinations. 40 passed the first, 39 passed the second

and 48 passed the third. 19 passed all three 9 passed first two but failed in the third,

19 failed in the first two and passed the third. Find how many children passed

at least two exams.

1. b) For a random sample of 10 persons fed on diet A, the increase in weights are

10, 6, 16, 17, 13, 12, 8, 14, 15, 9.For another random sample of 12 persons fed on

diet B the increase in weights are 7, 13, 22, 15, 12, 14, 18, 8, 21, 23, 10, 17.

Test whether there is any significant difference between the diets.           ( 10 + 10 )

22) a) The following data show the values of sample mean X and range R for 10 samples

of size 8 each. Calculate the control limits for mean and range

Sample no	1	2	3	4	5	6	7	8	9	10
mean	11.2	11.8	10.8	11.6	11	9.6	10.4	9.6	10.6	10
range	7	4	8	5	7	4	8	4	7	9

Determine whether the process is in control.

 

1. b) A tea company appoints 4 salesmen A, B, C, and D and observes their sales in

three seasons summer, winter, monsoon. The figures are given below.

	A	B	C	D
summer	36	36	21	35
winter	28	29	31	32
monsoon	26	28	29	29

Test whether there is significant difference

1.  i) among salesmen
2. ii) among seasons.                                                                  ( 10 + 10 )

 

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YB 14

          LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.COM. DEGREE EXAMINATION – COMMERCE

FOURTH SEMESTER – April 2009

              ST 4205/ ST 4200 – ADVANCED STATISTICAL METHODS

 

 

 

Date & Time: 27/04/2009 / 9:00 – 12:00          Dept. No.                                                  Max. : 100 Marks

 

 

PART-A

          Answer all the questions                                                                     (10 x 2 = 20)

 

• When do you say that two attributes are independent?
• From the following data find out the missing frequencies. (AB) = 100, (A) = 300, N = 1000,

(B)=600.

• A bag contains 5 white and 3 black balls. Two balls are drawn one by one without replacement.

What is the probability that both are white?

• State the addition theorem for two events.
• State the properties of normal distribution
• What is standard error?
• Define type I error and type II error.
• What are the control limits for a p- chart?
• Explain briefly the term confidence interval.
• State any two uses of t- distribution.

 

PART-B

Answer any 5 questions                                                                                          (5 x 8 = 40)        

• According to a survey the following results were obtained.

No of students appeared	800
married	150
Married and successful	70
Unmarried and successful	550

Compute Yules coefficient of association and comment on the results.

• A committee of 4 persons is to be appointed from 3 Indians 4 Americans and 2 Japanese and

1 Pakistani.  Find the probability of forming the committee in the following manner.

1. there must be 1 from each group
2. it should have atleast 1 from Americans

• Pakistani must be there in the committee.
• The incidence of a certain disease is such that on the average 20%of the workers suffers

from it.  If 10 workers are selected at random, find the probability that are

1. exactly two workers will suffer from the disease
2. no worker will suffer from the disease

• not more than two workers will suffer from the disease
• Explain the method of analysis of variance for two way classification.
• Explain the theory of control charts.
• An experiment was conducted to study the effectiveness of a new drug. 300 patients were

treated with new drug and 200 were not treated with the drug. The results of the experiment

are given below.

Details	cured	Condition worsened	No effect
Treated with drug	200	40	60
Not Treated with drug	120	30	50

Test the effectiveness of the drug.

• In a distribution exactly normal, 5% of the items are under 35 and 65% are under 63.

What is the mean and SD of the distribution?

• The wages of 10 workers taken at random from a factory are given below.

578, 572, 570, 568, 572, 578, 570, 572, 596, 584.

Is it possible that the mean wage of all workers of this factory is Rs 580?

 

PART-C

Answer any 2 questions                                                                                            (2 x 20 = 40)

 

• a) The following table gives the number of days in a 50-day period during which

automobile accidents occurred in a city.

No of accidents	0	1	2	3	4
No of days	21	18	7	3	1

Fit a Poisson distribution to the data.

19. b) A company has two plants to manufacture scooters. Plant I manufactures 70% of the

scooters and plant II manufactures 30%. At plant I 80%of the scooters are rated standard

quality and at plant II 90% of the scooters are rated standard quality. A scooter is picked up

at random and is found to be of standard quality. What is the chance  that it has come from

plant I or plant II .                                                                                                      ( 12 + 8 )

• a) Intelligence test of two groups of boys and girls  gave the following results:

 

	Mean	SD	Sample size
girls	75	15	150
boys	70	20	250

Test whether then mean marks of boys and girls are same.

 

1. b) In a  random sample of 600 men taken from a big city 400 are found to be smokers. In another

random sample of 900 men taken from another city 450 are smokers. Do the data indicate

there is a significant difference in the habit of smoking in the 2 cities?                   ( 10 + 10 )

 

21) a) Find all the ultimate class frequencies from the following data.

N = 800, (A) = 224,   (B) = 301, (C) = 150,   (AB) = 125, (AC) = 72, (BC) = 60, (ABC) = 32.

 

1. b) The following data show weekly sales before and after recognition of the sales organization.

 

Week no	1	2	3	4	5	6	7	8	9	10
Sales before	15	17	12	18	16	13	15	17	19	18
Sales after	20	19	18	22	20	19	21	23	24	24

Test whether there is any significant difference in sales before and after recognition of the

sample company.                                                                                                     ( 10 + 10 )

 

22) a) Assume that 15 litre milk bottles are selected at random from a process. The number

of air bubbles (defects) observed from the bottles is given below.

Draw a suitable control chart.

 

Bottle Number	Number of defects
1	4
2	5
3	7
4	3
5	3
6	5
7	6
8	2
9	4
10	8
11	3
12	5
13	4
14	3
15	4

 

1. b) A manufacturing company has purchased 3 new machines of different makes and wishes

to determine whether one of them is faster than the other in producing a certain output.

Five hourly production figures are observed at random from each machine and the results

are given below.

Machines

Makes	A1	A2	A3
1	25	31	24
2	30	39	30
3	36	38	28
4	38	42	25
5	31	35	28

Use analysis of variance and test whether there is any significant difference among the

machines.                                                                                                                    ( 10 + 10 )

 

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