Semester - IV Syllabus


B.Sc. II Year, IV Semester (CBCS): Statistics Syllabus
Paper-IV: Inference (DSC-2D)
(4 HPW with 4 Credits and 100 Marks)

Unit –I
Concepts of statistical hypothesis, null and alternative hypothesis, critical region, two types of errors, level of significance and power of a test. One and two tailed tests, test function (nonrandomized and randomized). Statement and Proof of Neyman-Pearson’s fundamental lemma for Randomized tests. Examples in case of Binomial, Poisson, Exponential and Normal distributions and their powers.
Unit II
Large sample tests for single sample mean, difference of means, single sample proportion,
difference of proportions and difference of standard deviations. Fisher’s Z-transformation for population correlation coefficient(s) and testing the same in case of one sample and two samples. Definition of order statistics and statement of their distributions.

Unit – III
Tests of significance based on χ 2 : χ2 - test for specified variance, goodness of fit and test for
independence of attributes (rxs, 2xk and 2x2 contingency tables). Tests of significance based on student’s – t: t-test for single sample specified mean, difference of means for independent and related samples, sample correlation coefficient. F-test for equality of population variances.

Unit – IV
Non-parametric tests: their advantages and disadvantages, comparison with parametric tests.
Measurement scale- nominal, ordinal, interval and ratio. Use of Central Limit Theorem in testing. One sample runs test, sign test and Wilcoxon-signed rank tests (single and paired samples). Two independent sample tests: Median test, Wilcoxon –Mann-Whitney U test, Wald Wolfowitz’s runs test. Use of central limit theorem in testing.


Reference Books:
1. V.K.Kapoor and S.C.Gupta: Fundamentals of Mathematical Statistics, Sultan
Chand&Sons, New Delhi
2. Hogg, Tanis, Rao. Probability and Statistical Inference.7th edition. Pearson
Publication.
3. Parimal Mukhopadhyay: Mathematical Statistics. New Central Book agency.


Practical Paper – IV
(With 2 HPW, Credits 1 and Marks 25)

1. Large sample tests for mean(s), proportion(s), Standard deviation(s) and correlation coefficient.
2. Small sample tests for single mean and difference of means and correlation coefficient.
3. Paired t-test.
4. Small sample tests for mean(s), paired t-test and correlation coefficient using MS Excel.
5. Small sample test for single and difference of variances.
6. Small sample test for single and difference of variances using MS Excel.
7. χ2 – test for goodness of fit and independence of attributes.
8. χ2 – test for goodness of fit and independence of attributes using MS Excel.
9. Nonparametric tests for single and related samples (sign test and Wilcoxon signed rank test) and one sample runs test.
10. Nonparametric tests for two independent samples  (Median test, Wilcoxon Mann Whitney -U test, Wald - Wolfowitz’s runs test)

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