THE BOOK STATICS AND NUMERICAL METHODS HAVE FOLLOWING INDEX:

Unit 1 Testing of Hypothesis

Sampling distributions - Tests for single mean, Proportion, Difference of means (large and small samples) Tests for single variance and equality of variance -chi-square test for goodness of fit - Independence of attributes.

Unit II Design of Experiments

Completely randomized design - Randomized block design - Latin square design -22-factorial design.

Unit III Solution of Equations and Eigenvalue Problems

Newton-Raphson method - Gauss Elimination method - Pivoting - Gauss-Jordan methods - Iterative methods of Gauss-Jacobi and Gauss-Seidel - Matrix Inversion by Gauss-Jordan method - Eigenvalues of a matrix by Power method.

Unit IV Interpolation, Numerical Differentiation and Numerical Integration

Lagrange's and Newton's divided difference interpolation - Newton's forward and backward difference interpolation Approximation of derivatives using interpo-lation polynomials - Numerical integration using Trapezoidal and Simpson's 1/3 rules.

Unit V Numerical Solution of Ordinary Differential Equations

Taylor's series method - Euler's method - Modified Euler's method - Fourth or-der Runge-Kutta method for solving first and second order equations - Milne's predictor-corrector methods for solving first order equations Finite difference methods for solving second order equation.

Testing the hypothesis:

1st concept is hypothesis and acceptance

there are two kind of errors and two decisions , thus

1. Hypothesis true and test accepts.
2. Hypothesis true and test rejects.
3. Hypothesis false and test accepts.
4. Hypothesis false and test rejects.

there are two types of hypothesis:

1. Null hypothesis H⁰
2. Alternative hypothesis H¹

first null hypothesis is to be tested

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important terms:

1. prob.(reject if h⁰ true) = alpha i.e producer’s risk
2. prob.(accept if h⁰ false) = beta i.e consumer’s risk

Next concept is critical region and level of significance

rejection of H⁰ is critical region and the prob. alpha that any value of the statics belongs to critical region is level of significance.

usually level of significance is 5 percent and 1 percent.

Based on criticality, the test can be left tailed , right tailed or two tailed.

Tailing of samples

Now to test a hypothesis , we will need critical values /significant values. These are the value between accepted and critical region. This is different at 1 , 2 , 5 , 10 percent level of significance.

Large population

The hypothesis may be tested for whole population, for population mean , stsndard deviations and even difference between means and standard deviations.

Small population

The degree of freedom is to be analysed in case of small population. if n is no. of observations, k is no. of independent constraints than n-k is degree of freedom

n and deviation t distribution

t distribution test , paired t test to find difference between two means.

f distribution

used to verify equality of two variances.

x²

next os chi square test used to test goodness of fit

this is for 1st unit next is