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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) | (þi) |
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 |