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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.
- there must be 1 from each group
- 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
- exactly two workers will suffer from the disease
- 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.
- 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.
- 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.
- 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 |
- 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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