LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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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
- b) one is white and one is black
- 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
- i) no defective screw?
- 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.
- 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.
- 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.
- 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.
- 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
- i) among salesmen
- ii) among seasons. ( 10 + 10 )
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