LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Com. DEGREE EXAMINATION – COMMERCE
SUPPLEMENTARY EXAMINATION – JUNE 2008
ST 4205 / 3200 / 4200 - ADVANCED STATISTICAL METHODS
Date : 26-06-08
Time : 9:00 - 12:00
Dept. No.
Max. : 100 Marks
SECTION A
Answer all questions.
(10 x 2 = 20)
1. Mention the difference between correlation and association.
2. What is a contingency table?
3. Two balls are drawn without replacement from a bag containing 8 red and 7 white balls. Find the
probability that one is red and the other is white.
4. Give any two properties of normal distribution.
5. Define Parameter and Statistic.
6. A sample of 50 taken from a normal population with standard deviation 2 gave the mean 10. Can
it be concluded that the mean value of the population is 12? Test at 5% level.
7. Define Null and Alternate hypotheses.
8. Let X be a random variable with the following distribution function:
X:
-1
0
1
2
P[X=x]:
0.2
0.3
0.4
0.1
Find the variance of 2X+3.
9. In one way Analysis of Variance with 5 treatments and 20 observations, the total sum of squares
and treatments sum of squares are obtained respectively as 320 and 188. What is the value of Fratio?
10. What are Control Charts?
SECTION B
Answer any FIVE questions.
(5 x 8 = 40)
11. Find all the ultimate class frequencies from the following data and verify whether or not the data
is consistent.
N=800, (A)=224, (B)=301, (C)=150, (AB)=125, (AC)=72, (BC)=60, (ABC)=32.
12. a.) Define conditional probability of two events A and B.
b.) In a bolt factory, machines A, B and C manufacture respectively 25%, 30% and 40% of the
output of which 5%, 4% and 2% are defective bolts. A bolt is drawn at random and is found to be
defective. What is the probability that it was manufactured by machine A?
13. Out of 800 families with 4 children each, what percentage would be expected to have a.) 2 boys
and 2 girls b.) no girls c.) atleast one boy? Assume equal probabilities for boys and girls.
14. In City A, out of a random sample of 1000 persons 100 were found to be vegetarians while in City
B out of a random sample of 1500 persons 180 were found to be vegetarians. Test at 1% level
whether the proportion of vegetarians in the two cities are equal.
15. Explain the concept of Analysis of Variance with an example.
16. Let X be a random variable with probability mass function :
X:
2
4
6
8
P[X=x]:
0.4
0.15 0.2
0.25.
Find the distribution of the standardized variable Z and show that its mean and
variance are 0 and 1 respectively.
17. Write short notes on the following:
a.) Point and interval estimation
b.) Sampling Distribution.
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18. The following data gives the number of defective spark plugs in 10 lots of 100 spark plugs each:
Lot: 1
2
3
4
5
6
7
8
No. of defectives: 5
10
12
8
6
5
6
3
Lot: 9
10
No. of defectives: 3
5
Construct an appropriate control chart and interpret the results.
SECTION C
Answer any TWO questions.
(2 x 20 = 40)
19. a.) An automobile company gives the following information about age groups and the liking for
particular model of car:
Age group
Liked the model
below 20
20 – 39
40 – 59
60 and above
Yes
140
80
40
20
No
60
50
30
80
Calculate the coefficient of Contingency and comment whether there is association
between the age group and liking the model.
b.) Of 120 students in a class, 60 are studying French, 50 are studying Spanish
and 20 are studying both French and Spanish. A student is chosen at random. Find
the probability that the student is studying i.) French or Spanish ii.) neither
French nor Spanish iii.) only French and iv.) exactly one of the two languages.
(12+8)
20. a.) The following table shows the number of customers returning a certain type of product due to
dissatisfaction in a sales division. The data is for 100 stores:
No. of returns: 0
1
2
3
4
5
6
No. of stores: 4
14
23
23
18
9
9
Fit a Poisson distribution to the above data.
b.) A sample of 100 dry battery cells tested to find the length of life gave the
mean life as 12 hours with a standard deviation of 3 hours. Assuming the data
to be normally distributed, what percentage of battery cells are expected to
have life i.) more than 15 hours ii.) less than 6 hours and iii.) between 10 and
14 hours?
(12+8 )
21. a.) Two types of drugs were used on 8 and 7 patients for reducing the weight.
Drug A was imported and Drug B indigenous. The decrease in the weight (in kgs)
after using the drugs for six months was as follows:
Drug A:
9
11
13
11
15
9
12
14
Drug B:
10
12
10
14
9
8
10
Is there a significant difference in the efficacy of the two drugs as regards the
decrease in weight? Test at 5% level.
b.) In a hospital 480 female and 520 male babies were born in a week. Do these
data support the hypothesis that male and female babies are born in equal
number? Test at 5% level.
(12+8)
22. The following table gives the monthly sales (in thousands rupees) of a certain firm in 3 states by
its 4 salesmen:
Salesmen
States
1
2
3
4
A
6
5
3
8
B
8
9
6
5
C
10
7
8
7
Test at 5% level whether the mean sales made by the salesmen are same and the
mean sales across states are same.
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