INFERENTIAL STATISTICS

UNIT-I [8 Hours]
Introduction to Statistical Inference
Introduction to statistical hypothesis, types of hypothesis - simple and composite, fundamental concepts of null hypothesis, alternative hypothesis, one-tailed and two-tailed test, small sample and large sample test, critical region, acceptance region, critical value, type I error and Type II error, importance of type one and type two error, level of significance, confidence level, Steps involved in testing of hypothesis. Introduction to parameter estimation, point estimation, interval estimation, properties of good estimator -unbiasedness, consistency, efficiency and sufficiency,

UNIT-II [8 Hours]
Testing of Hypothesis: Parametric Test Test for the mean of normal
distribution, test for the equality of two and more normal distributed populations, test for the variance of normal distribution, test for the equality of two or more than two normal distributions, the confidence interval for population arithmetic mean, confidence interval for population variance. t-Test for single and 2 means, f-test, Introduction to ANOVA.

UNIT-III [10 Hours]
Testing of Hypothesis: Non-Parametric test:
Introduction' to non-parametric test, run test, Wilcoxon signed Rank Test, Wilcoxon Matched signed pair rank test, Mann-Whiteney U test, Kruskal Wallis test, Fried Man Rank Test for small sample and large sample, Goodness of fit test and independence of attributes using x2 test, testing of equality of more than two variances using x2 test.

UNIT-IV [9 SESSIONSI
Parameter Estimation;[9 Hours]
Method of estimation - maximum likelihood estimation, properties of method of maximum likelihood estimator, estimation of mean and variance of normal distribution using maximum likelihood estimator, introduction and assumptions of ordinary least square method, estimation of parameters in multiple linear regression coefficients, properties of the OLS method. Method of minimum Chi-Square, confidence interval estimation of for the parameter estimated through minimum Chi-Square method, method of moments, estimation of parameters using method of moments, properties of method of moments.

UNIT-V [10 Hours]
Bavesian Statistical Inference
Bayes Theorem, Introduction to Bayesian statistical inference, Bayesian Procedures – Prior and posterior distributions, point estimation of Bayesian statistic, Bayesian Interval estimation, Bayesian testing procedures, Bayesian sequential procedures, important terms related to Bayesian statistical inference, introduction to moderm Bayesian statistical inference, simple problems related to Bayesian inference and estimations.