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Note: i) Attempt TWO Questions in all. ii) FOUR marks are reserved for PRACTICAL NOTE BOOK and FIVE for VIVA VOCE.

1. A population consists of five numbers 2, 4, 6, 8, 10. Draw all possible samples of size n = 3 with replacement. Find the sample mean (x ) and sample median (~x ) for each sample. Make the sampling distribution of x and ~x . Show that: i) ì=ì ii) ì=Population Median x)<Variance( ~ 2,3,3

iii) Var( — x )

X X

2. A metalurgist has collected the following data on the thermal expansion of two different alloys A and B.

Alloy A 18.1, 13.8, 21.5, 18.1, 20.1,23.6, 19.7, 21.7, 18.6, 24.8, 19.2, 15.4, 18.5, 22.5, 21.1, 21.0, 22.3, 19.5, 13.2, 25.6, 19.5, 18.0, 16.9, 25.1, 30.1, 18.2, 25.8
Alloy B 16.1, 18.9, 20.5, 17.2, 23.8, 19.2, 15.3, 18.0, 15.9, 16.2, 12.0, 19.4, 15.6, 17.6, 22.7, 17.2, 18.4, 17.9, 22.3, 19.1

a) Test the equality of variances. b) Test the equality of means. c) Compute 80% confidence interval for the difference between two means. 3,3,2

3. Worms are classified into five groups. A random sample of 10 worms is taken from each group. The length of each worm is measured. The results are shown in the following table.

Length Groups
G1 G2 G3 G4 G5
8.3 9.0 8.6 10.1 8.0
7.1 7.1 8.3 12.0 8.8
7.1 10.1 9.4 12.2 10.5
9.6 9.9 11.6 11.4 14.1
10.3 9.6 12.1 9.8 9.8
8.6 7.3 12.1 10.2 10.0
7.1 10.6 11.6 10.0 9.6
7.3 8.8 10.7 8.6 9.5
9.1 8.1 8.9 12.2 9.0
8.6 10.1 8.4 9.8 11.1

a) Setup the ANOVA table and test the hypothesis that mean length in each group is same. 6 b) Apply Duncan’s multiple Range test if applicable. 2

4. Given the following data: a) Find age specific death rate in standard population. 2 b) Find crude death rate of standard population. 1 c) Find standardized death rate by indirect method. 5

Age Group Standard Local Population
ƒ Population (Pi) Death (Di) i)
0 – 1 1831 260 831
1 – 5 1761 252 726
5 – 10 9005 115 920
10 – 15 8205 192 1025
15 – 20 5852 98 1201
20 – 30 10635 123 3148
30 – 40 9001 116 1142
40 – 50 6732 112 850
50 – 60 4135 115 630
60 and over 4060 225 600

*** B.A/B.Sc-II (10/A) P-xvii ***

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last updated on 19-06-2016