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B.E./B.Tech. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2010

Fourth Semester

Mechanical Engineering

MA2266STATISTICS AND NUMERICAL METHODS(Common to Automobile Engineering and Production Engineering)

(Regulation 2008)

(Statistical Tables may be permitted)

Time : Three hours Maximum : 100 Marks

Answer ALL questions

PART A(10 x 2 = 20 Marks)

1)

What are parameters and statistics in sampling?

2)

Write any two applications of2

-test.

3)

Compare one-way classification model with two-way classification model.

4)

What is meant by Latin square?

5)

Write the convergence condition and order of convergence for Newton-Raphson

method.

6)

Compare Gauss Jacobi with Gauss Jordan.

7)

Create a forward difference table for the following data and state the degree of

polynomial for the same.

:x 0 1 2 3

( ) :y f x -1 0 3 88)

Compare Simpsons 1/3 rule with Trapezoidal method.

9)

Using Taylors series find (0.1)y for 1 , (0) 0dy

y ydx

.

10)

Solve2

4 0x x

y y

.

PART B(5 x 16 = 80 Marks)

11)

(a) (i) A machine produces 16 imperfect articles in a sample of 500. After machine is

overhauled, it produces 3 imperfect articles in a batch of 100. Has the machine been

improved?

(a) (ii) Examine whether the difference in the variability in yields is significant at 5% level

of significance, for the following.

Set of 40 plots Set of 60 plots

Mean yield per plot 1256 1243

S.D. per plot 34 28

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(Or)

(b) (i) Test if the difference in the means is significant for the following data:

Sample I: 76 68 70 43 94 68 33

Sample II: 40 48 92 85 70 76 68 22

(b) (ii) The following data gives the number of aircraft accidents that occurred during the

various days of a week. Find whether the accidents are uniformly distributed over the

week.

Days: Sun Mon Tue Wed Thu Fri Sat

No. of accidents: 14 16 8 12 11 9 14

12)

(a) Carry out ANOVA (Analysis of variance) for the following.

Workers

A B C D

1 44 38 47 36

2 46 40 52 43

3 34 36 44 32

4 43 38 46 33

5 38 42 49 39

(Or)

(b) Perform Latine Square Experiment for the following.

Roam I II III Three equally spaced

concentrations of poison asextracted from the scorpion fish.

Arabic 1 2 3 Three equally spaced body

weights for the animals tested.

Latin A B C Three equally spaced times of

storage of the poison before it is

administered to the animals.

I II III

1. 0.194 0.73 1.187

A B C

2. 0.758 0.311 0.589

C A B

3. 0.369 0.558 0.311

B C A

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13)

(a) (i) Find the inverse of

0 1 1

1 2 0

3 1 4

A

using Gauss-Jordon method.

(a)

(ii) Solve by Gauss-Seidel method

6 3 12 35;x y z

8 3 2 20;x y z

4 11 33x y z

.

(Or)

(b)

(i) Using Gauss-Jordan, solve the following system 10 12;x y z

2 10 13;x y z 5 7x y z .

(ii) Find all the Eigen value of

1 6 1

1 2 0

0 0 3

A

using power method. Using

1 1,0,0

T

x

as initial vector.

14)

(a) (i) Taking10

h

, evaluate

0

sin x dx

by Simpsons 1/3 rule. Verify the answer with

integration.

(ii) Use Lagranges formula to fit a polynomial to the following data hence find

( 1)y x .

:x - 1 0 2 3:y - 8 3 1 12

(Or)

(b)

(i) Evaluate

6

2

0

1

1dx

xusing Trapezoidal rule. Verify the answer with direct

integration.

(ii) Find

1976y from the following

:x 1941 1951 1961 1971 1981 1991:y 20 24 29 36 46 51

15)

(a) (i) Use Eulers method, with 0.1h

to find the solutio of 2 2y x y

with

(0) 0y in 0 5x .

(ii) Using Milnes method, obtain the solution of2dy

x ydx

at 0.8x given (0) 0y ,

(0.2) 0.02, (0.4) 0.0795, (0.6) 0.1762y y y .

(Or)

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(b)

(i) Use R.K Method fourth order to find the (0.2)y if2 ,

dyx y

dx

(0) 1, 0.1y h .

(ii) Solve 2 14 4 2n

n n nu u u .