Perform an analysis of the variance on these data and show that significance test does not reject their homogeneity.
10
Explain the terms main effect and interactions in factional experiments. A complete 23 experiment is replicated r times. Describe the procedure for testing the presences of different main effects and interactions. 10
8. If the population consists of a linear trend, than prove that
V(ys t V(ys ys V(yn)random. 12

What are Ratio and regression estimates Define.


What is Likelihood Ratio test Explain. Give its properties. 12


Also give Biases of the ratio and regression estimators. 8
9. Define the concepts of
Sampling distribution and standard error
Null and Alternative hypothesis
Type I and Type II errors and
Critical region and level of significance. 8

10. Explain Wald Wolfowitz run test. Mention their usefulness. 8
Let X have the distribution .x (1œ.)1œx,
x 0 . 1. For testing H0 . .0 against H1 . .1 construct SPRT and obtain its O.C. function. 12
GDB-15783 4 400

Roll No. ............................ Total No. of Pages 4

1(ADS)1 STATISTICS-I X-O

Time Three Hours] [Maximum Marks 100 Note Each question or part thereof shall begin on a fresh page.
Your answers should be precise and coherent.
Attempt any FIVE questions.

1. Given log10 654 2.8156, log10 658 2.8182,
log10 659 2.8189, log10 661 2.8202 find log10 656. 10
Find f (7.60) from the following table
x 7.47 7.48 7.49 7.50 7.51 7.52 7.53
193 195 198 201 203 206 208 10

2. An urn contains 9 balls, two of which are red, three blue and four black. Three balls are drawn from the urn at random. What is the probability that

the balls are of different colours


two balls are of the same colour and third is of different colour


the three balls are of the same colour 10
The chances that doctor A will diagnose a disease X correctly is 60%. The chances that a patient will die by his treatment after correct diagnosis is 40% and the chance of death by wrong diagnosis is 70%. A patient of a doctor who had disease died. What is the chance that his disease was diagnosed correctly 10

GDB-15783 1 Contd.
3. State and prove Chebychev's inequality. 10

A symmetric die is thrown 600 times. Find the lower bound for the probability of getting 80 to 120 sixes. 4


A box contains white and black balls. balls are drawn at random. Find the expected value of the number of white balls drawn. 6


4. Find the moment generating function of the standard binomial
œ np)variate


and obtain its limiting form as n . 8. 8
npq
Show that for the bivariate normal distribution
. 12 2 .
dp const.exp œ œ 2.xy y dxdy,
. 2 .
. 2(1œs .
Moment generating functions is
.12 2 .
M t2) exp (t1 2. t1 t2 t2) .
. .
.2 .

Also show that, the moments obeying the recurrence relation µ s œ 1).µ rœ1, sœ1+ œ œ .2)µ rœ2, sœ2.
rs

12
5. A sample of 800 families with four children each revealed the following distribution No. of sons: 0 1 2 3 4 No. of girls: 4 3 2 1 0
No. of families 32 178 290 236 64 Is this result consistent with the hypothesis that male and female births are equally probable 10
GDB-15783 2 Contd.
Batches

1 1610 1610 1650 1680 1700 1720 1800
2 1580 1640 1640 1700 1750
3 1460 1550 1600 1620 1640 1660 1740 1820
4 1510 1520 1530 1570 1600 1680


GDB-15783

The heights of six normally chosen sailors are (in inches) 63, 65, 68, 69, 71 and 72. Those of 10 randomly chosen soldiers are 61, 62, 65, 66, 69, 69, 70, 71, 72 and 73. Discuss, the light that these data throw on the suggestion that sailors are on the average taller than soldiers (significant value at level of significance for 14 degrees of freedom is 1.76).
10

6. The equation of two regression lines obtained in a correlation analysis of 60 observations are
5x 6y 24 and 1000 y 768x œ 3708.
What is the correlation coefficient and what is its probable
error

Show that the ratio of the coefficient of variability of x to that y is 5/24. 8
Following are the means, standard deviation and correlation of X1 seed by crop in units per acre, X2 spring rainfall in inches, X3 accumulated temperature above 42 oF in spring, in a certain district of England during twenty years
X 28.02, X =4.91, X =594
1 23
s = 4.42,s=1.0,s= 85
1 23
r .80, r œ .4, r œ 0.56.
12 13 23
Find the partial correlations and the regression equation for hay-crop on spring rainfall and accumulated temperature. 12

7. The following table shows lives in hours for four batches of electric lamps
Lives in hour

3 Contd.