MA1254 -STATISTICS AND NUMERICAL METHODS Questions Bank 2014

Anna University, Chennai

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SRINIVASAN ENGINEERING COLLEGE, PERAMBALUR

MA1254 -STATISTICS AND NUMERICAL METHODS

QUESTION BANK

PART – B

UNIT I

1.Car stereo manufacturer of A have mean life time of 1400 hrs with S.D of 200 hrs while those

of manufacturer B have mean lifetime of 1200 hrs with S.D of 100 hrs. If a random

sample of 120 stereos of each manufacturer are tested. i) What is the probability that the

manufacturer of A’s stereo’s will have a mean life time of at least 160 hrs more than the

manufacturer B’s stereo’s ii) and 250 hrs more than the manufacturer B stereo’s.

2. In a sample of 1000 people in Mumbai, 540 are rice eaters and the rest are wheat eaters. Can

we assume that both rice and wheat are equally popular in this state at 1% LOS?

3. In a test given of two groups of students the marks obtained were as follows.

I Group: 18 20 36 50 49 36 34 49 41

II Group: 29 28 26 35 30 44 46

Examine the significant difference between the means of marks secured by students of the above 2 groups.

4. The weight gains in pounds under two systems of feeding of calves of 10 pairs of identical

twins is given below.

Twin pair: 1 2 3 4 5 6 7 8 9 10

System A: 43 39 39 42 46 43 38 44 51 43

System B: 37 35 34 41 39 37 37 40 48 36.

Discuss whether the difference between the 2 systems of feeding is significant.

5.Two random samples gave the following results;

Sample

Size

Sample mean

Sum of squares of deviations from the mean

1

10

15

90

2

12

14

108

Test whether the samples come from the same normal population at 5% LOS.

6. 4 coins were tossed 160 times and the following results were obtained.

No of heads: 0 1 2 3 4

Observed Fr:17 52 54 31 6

Under the assumption that the coins are balanced, find the expected frequencies of getting

0, 1,2, 3,4 heads and test the goodness of fit.

7.A sample of 200 persons with a particular disease was selected. Out of these , 100 were given a

drug and the others were not given any drug. The result are as follows:

No of persons

Drug

No Drug

Total

Cured

65

55

120

Not cured

35

45

80

Total

100

100

200

Test whether the drug is effective or not.

  1. The following data relate to a random sample of government employees in 2 states of the Indian Union.

Sample

Size

Mean monthly income of the employees

Variance

1

16

440

40

2

25

460

42

Test whether the samples come from the same normal population

  1. A normal population has a mean of 6.48 and S.D of 1.5 . In a sample of 400 members mean is 6.75 .I s the difference significant?
  1. A simple sample of heights of 6400 English men has a mean of 170 cm and S. D of 6.4 cm, while a simple sample of heights of 1600 Americans has a mean of 172 cm and a S.D of 6.3 cm. Do the data indicate that Americans are, on the average , taller than the Englishmen?
  1. 1000 students at college level were graded according to their I.Q and their economic conditions. What conditions can U draw from the following data:

Economic conditions

I.Q level

High

Low

Rich

460

140

Poor

240

160


UNIT – II

1. The following are the number of mistakes made in 5 successive days by 4 technicians working for a photographic laboratory. Test whether the difference among the 4 sample means can be attributed to chance. LOS at 1%.

Technician

I

II

III

IV

6

14

10

9

14

9

12

12

10

12

7

8

8

10

15

10

11

14

11

11

2. Set up the analysis of variance for the following results of a Latin square design at 1% LOS.

A 12

C 19

B 10

D 8

C 18

B 12

D 6

A 7

B 22

D 10

A 5

C 21

D 12

A 7

C 27

B 17

3. To study the performance of 3 detergents and 3 different water temperatures, the whiteness readings were obtained with specially designed equipment.

Detergent

Water temp

A

B

C

Cold water

57

55

67

Warn water

49

52

68

Hot water

54

46

58

Perform a 2 way analysis of variance using 5 % LOS.

4. The following data are obtained from a clip_image002 factorial experiment blocked 3 times. Evaluate the sum of squares for all factorial effect by the contrast method. Draw conclusion.

Blocks

Treatment combination

I

II

III

(1)

12

19

10

k

15

20

16

p

24

16

17

kp

24

17

29

5.Perform two way ANOVA for the given below:

Treatments

Plots of land

A

B

C

D

I

38

40

41

39

II

45

42

49

36

III

40

38

42

42

6.Analyze the variance in LSD .

S122

P121

P123

Q122

Q124

R123

P122

S125

P120

Q199

S120

R121

R122

S123

Q121

P122

7. The following data are obtained from a clip_image002[1] factorial experiment blocked 3 times. Evaluate the sum of squares for all factorial effect by the contrast method. Draw conclusion.

Blocks

Treatment combination

I

II

III

IV

(1)

12

12.3

11.8

11.6

k

12.8

12.6

13.7

14

p

11.5

11.9

12.6

11.8

kp

14.2

14.5

14.4

15

8. Find ANOVA using CRD.

Samples

8

7

12

10

5

19

7

10

13

14

9

12

11

9

14

9. Perform two way ANOVA for the given below:

Water temp

Detergent A

Detergent B

Detergent C

Cold

57

55

67

Warm

49

52

68

Hot

54

46

58

10.Perform ANOVA for the given below using CBD method.

A6

C5

A8

B9

C8

A4

B6

C9

B7

B6

C10

A6


Unit 3

1. Solve the system of equations by Gauss Elimination method. 10 x- 2y +3z =23;

2 x+10 y -5z = - 33; 3x -4y +10 z =41.

2. Find the iterative formula for finding the value of clip_image004 where N is a real number , using Newton –

Raphson method also find 1/26.

3.Solve the following system of equations by Gauss – Jacobi method

27 x +6y –z =85; x + y +54 z =110; 6x +15 y +2z =72.

4.Using power method , find the eigen value of A =clip_image006

5. Solve the system of equations by Gauss Jordan method

3x+ y – z = 3; 2x – 8y + z = -5; x -2y + 9z = 8

6.Solve the following system of equations by Gauss – Seidel method

4x + 2y + z =14; x + 5y – z =10; x + y +8z =20.

7.Find the inverse of the matrix clip_image008

8.Find the dominant of eigen value and eigen vector of A =clip_image010

9.Compute the real root of x log x =1.2 using Newton’s Raphson method.

10. Find the inverse of clip_image012


Unit 4

1.The following table gives the population of a town during the last 6 census. Estimate using Newton’s

interpolation formula, the increase in the population during the period 1946 to 1948.

Year

1911

1921

1931

1941

1951

1961

Population(in 1000’s)

12

13

20

27

39

52

2.By dividing the range into 10 equal parts, evaluate clip_image014by using Simpson’s 1/3 rule.

3.Using the data given below find the value of clip_image016 by Trapezoidal rule.

X

1

2

3

4

5

6

7

8

9

Y

2.061

2.312

2.891

3.106

3.670

4.721

6.103

7.950

9.942

4.A rod is rotating in a plane about one of its ends. If the following table gives the angle clip_image018 radians through which the rod has turned for different values of time t seconds. Find it angular velocity and angular acceleration when t= 0.7 seconds.

t seconds

0.0

0.2

0.4

0.6

0.8

1.0

clip_image018[1]radians

0.0

0.12

0.48

1.10

2.0

3.20

5.Using Lagrange’s formula to calculate f(3):

x

0

1

2

4

5

6

F(x)

1

14

15

5

6

19

6..Find the cubic function from the following table:

x

0

1

3

4

F(x)

1

4

40

85

7.From the following table find clip_image020 at x = 43.

x

40

50

60

70

80

90

clip_image020[1]

184

204

226

250

276

304

8.Find the value of x = 2.5

x

0

1

2

3

4

y

7

10

13

22

43

9.Find the polynomial using Newton’s forward method.

x

4

6

8

10

y

1

3

8

16

10.Find the value of y’’ at the point x =0.96

X

0.96

0.98

1

1.02

1.04

F(x)

0.7825

0.7739

0.7651

0.7563

0.7473


Unit 5

1.Evaluate the values of y(0.1) given y’’ –clip_image022+clip_image024 =0 , y(0) =1, y’(0) =0 by using Taylor series

method.

2. Using Euler’s method solve y’ = x + y + xy, y(0) =1 . Compute y at x =0.1 by taking h =0.05

3. Using R.K method of 4th order solve clip_image026 with y(0) = 1 at x=0.2.

4. Consider the second order initial values problem y’’ -2y’ =clip_image028 sint with y(0)= -0.4 and

y’(0)= -0.6 using fourth order R.K method , find y(0.2)

5. Using Milne’s method find y(4.4) given 5xy’ + clip_image024[1]-2 = 0 given y(4) =1, y(4.1)=1.0049,

y(4.2) =1.0097 & y(4.3) = 1.0143

6. Solve the system equations clip_image030 with y(0) = 1, z (0) = 1 by taking h= 0.1 to get

y(0.1) and z(0.1) by Taylor series method.

7.Solve clip_image032 = 1- y , y(0) =0 by modified Euler’s method.

8.Using R.K method solve clip_image034 with y(0) = 1 at x= 0.2

9. Solve clip_image036 by

Milne’s method to find y(0.8) and y(1).

10. Using improved Euler’s method find y(0.2) and y(0.4) from y’ = x +y , y(0) = 1 with h =0.2.