Unit I (Testing of Hypothesis)

Transcription

1 SUBJECT NAME : Statistics and Numerical Methods SUBJECT CODE : MA645 MATERIAL NAME : Part A questions REGULATION : R03 UPDATED ON : November 07 (Upto N/D 07 Q.P) Unit I (Testing of Hypothesis). State level of significance and critical region.. What are parameters and statistics in sampling? 3. Mention the various steps involved in testing of hypothesis. 4. Define Type I error and Type II errors. 5. What are null and alternate hypothesis? 6. What are the applications of t -distributions? 7. Define Chi-Square test for goodness of fit. 8. State the application of Chi-square test. 9. Write the formula for the Chi-square test of goodness of fit of a random sample to a hypothetical distribution. 0. Give the formula for the - test of independence for a c b d. State the conditions for applying test.. What are the conditions for the validity of -test? 3. A random sample of 00 tins of coconut oil gave an average weight of 4.95 kgs. With a standard deviation of 0. kg. Do we accept that the net weight is 5 kgs per tin at 5% level? Sri Hariganesh Publications (Ph: , ) Page

2 4. Twenty people were attacked by a disease and only 8 survived. The hypothesis is set in such a way that the survival rate is 85% if attacked by this disease. Will you reject the hypothesis that it is more at 5% level ( z )? Unit II (Design of Experiments). State the basic principles of design of Experiments.. What do you understand by Design of an experiment? 3. What is the aim of the design of experiment? 4. State the assumptions involved in ANOVA. 5. Write down the ANOVA table for one way classification. 6. Define: RBD. 7. What is a completely randomized design? 8. State any two advantages of a Completely Randomized Experimental Design. 9. Discuss the advantages and disadvantages of Randomized block design. 0. Compare one-way classification model with two-way classification model.. Write any two differences between RBD and CRD.. Explain the situations in which randomized block design is considered an improvement over a completely randomized design. 3. What is meant by Latin square? 4. What are the advantages of a Latin square design? 5. Is Latin square Design possible? Why? 6. State the advantages of a factorial experiment over a simple experiment. 7. Define factorial design. Unit III (Solution of Equations and Eigen value Problems). What are the merits of Newton-Raphson method?. Mention the order and condition for the convergence of Newton-Raphson method. 3. What is the order of convergence and also state the error term for Newton Raphson method? Sri Hariganesh Publications (Ph: , ) Page

3 4. Find the real positive root of 3x cos x 0 by Newton s method correct to 6 decimal places. 5. Find a real root of the equation x e x, using Newton-Raphson method. 6. Using Newton-Raphson method, find the iteration formula to compute N. 7. Arrive a formula to find the value of 3 N, where N 0, using Newton-Raphson method. 8. Distinguish between Gauss elimination and Gauss-seidel methods. 9. Compare Gauss elimination and Gauss Jacobi methods. 0. Write down the iterative formula of Gauss-Seidal method.. Compare Gauss Jacobi with Gauss Jordan.. State the principle used in Gauss-Jordan method. (Procedure of Gauss-Jordan Method.) 3. Write the procedure involved in Gauss elimination method. 4. Solve the equations A B C 6, 3A 3B 4C 0, A B 3C 3 using Gauss elimination method. 5. Solve the following system of equations using Gauss-Jordan elimination method x y 3, x y. 6. Explain the power method to determine the eigenvalue of a matrix. 7. Find the dominant eigenvalue of the matrix 3 4 by power method. Unit IV (Interpolation, Numerical Differential & Integration). What is meant by interpolation?. What is the need of Newton s and Lagrange s interpolation formula? 3. State the formula to find the second order derivative using the forward differences. 4. Write down the Lagrange s interpolating formula for interpolation and state its uses. 5. State the use of Lagrange s interpolation form. Sri Hariganesh Publications (Ph: , ) Page 3

4 6. Use Lagrange s formula to fit a polynomial to the data and find y at x. x y Create a forward difference table for the following data and state the degree of polynomial for the same. x : 0 3 y f ( x) : State any two properties of divided differences. 9. Show that the divided difference of second order can be expressed as the quotient of two determinants of third order. 0. Form the divided difference table for the following data: x : 5 5 y : Find the area under the cure passing through the points 0,0,,,,.5, 3,.3, 4,, 5,.7 and. What is inverse interpolation? 6, Specify the Newton s backward difference formulae for dy and d y. 4. Compare Simpson s /3 rule with Trapezoidal method. 5. Write down the Simpson s /3 rule in numerical integration. 6. Write down the errors in Trapezoidal and Simpson s rules of numerical integration. 7. Evaluate 0.5 x by Trapezoidal rule, dividing the range into 4 equal parts. 8. Evaluate, using Trapezoidal rule, taking h 0.5. x 9. Using Trapezoidal rule, evaluate with h 0.. Hence obtain an approximate x 0 value of. Sri Hariganesh Publications (Ph: , ) Page 4

5 0. Evaluate I h , correct to three decimal places using trapezoidal rule with x Unit V (Numerical Solution of Ordinary Differential Eqns.). Bring out the merits and demerits of Taylor series method.. State the advantages of Runge-Kutta method over Taylor series method. 3. State the merits of RK method over Taylor series method. 4. Use the Runga-Kutta fourth order method to find the value of y when x given that y when x 0 and that dy y x. y x 5. Find y(0.) by Euler s method, if dy x y, y(0). 6. Using Euler s method, determine the value of y(0.0) if y ysubject to y(0). 7. State the modified Euler s formula for first order ordinary differential equation. 8. Compute y at x 0.5 by Modified Euler method given y xy, y(0). 9. Given dy x y, y(0). Determine (0.0) y using Euler s modified method. dy 0. Using Taylor s series find y(0.) for y, y(0) 0.. Using Taylor series method, find y at x 0.,0. given (correct to 4 decimal places).. Using Taylor s method, find y at x.given dy x y, y(0), dy 3 x y, y(). dy d y 3. Write the central difference approximations for,. 4. What is main difference between single and multistep methods in solving first order ordinary differential equation? Sri Hariganesh Publications (Ph: , ) Page 5

6 5. Convert the differential equation y ( x) y ( x) y 0 into finite difference equivalent form. 6. Solve y x 4y x 0. d y 7. Obtain the finite difference scheme for differential equation y Write the Milne s predictor-corrector formula All the Best---- Sri Hariganesh Publications (Ph: , ) Page 6