THIRD SEMESTER STATISTICS
Statistical Inference
UNIT-I
Concepts: Population, Sample, Parameter, statistic, Sampling distribution, Standard error. convergence in probability and convergence in distribution, law of large numbers, central limit theorem (statements only). Student’s t- distribution, F – Distribution, χ2-Distribution:Definitions, properties and their applications.
UNIT-II
Theory of estimation:Estimation of a parameter, criteria of a good estimator –unbiasedness, consistency, efficiency, &sufficiency and. Statement of Neyman’sfactorization theorem. Estimation of parameters by the method of moments and maximum likelihood (M.L), properties of MLE’s. Binomial, Poisson &Normal Population parameters estimate by MLE method. Confidence Intervals.
UNIT-III
Testing of Hypothesis:Concepts of statistical hypotheses, null and alternative hypothesis,critical region, two types of errors, level of significance and power of a test. One and two tailed tests. Neyman-Pearson’s lemma. Examples in case of Binomial, Poisson, Exponential and Normal distributions.
UNIT – IV
Large sample Tests:large sample test for single mean and difference of two means,confidence intervals for mean(s). Large sample test for single proportion, difference of proportions. standard deviation(s) and correlation coefficient(s).Small Sampletests: t-test for single mean, difference of means and paired t-test. χ2-test for goodness of fit and independence of attributes. F-test for equality of variances.
UNIT – V
Non-parametric tests- their advantages and disadvantages, comparison with parametric tests. Measurement scale- nominal, ordinal, interval and ratio. One sample runs test, signtest and Wilcoxon-signed rank tests (single and paired samples). Two independent sampletests: Median test, Wilcoxon –Mann-Whitney U test, Wald Wolfowitz’s runs test.