Inferential Statistics

Course Title: Inferential Statistics

Course No: BDS204

Nature of the Course: Theory + Lab

Semester: 3

Full Marks: 45 + 30

Pass Marks: 18 + 12

Credit Hours: 3

Course Description

This course focuses on inferential statistical techniques that are relevant to Data Science. The course covers random sampling & sampling distribution, estimation, testing of hypothesis, different statistical tests and their applications.

Course Objectives

Course Objectives:

After successful completion of the course, students will be able to

 Describe and calculate sampling distribution of sample mean, sample variance and sample proportion.

 Describe and apply the principles of inferential statistics.

 Understand and apply different statistical prospects of point estimation and interval estimation.

 Apply sample size estimation technique under different scenario.

 Explain the fundamental concepts of testing of hypothesis and linkage between confidence interval estimation and testing of hypothesis.

 Apply different statistical tests appropriately focusing in the research problems related to data science

Course Contents

1. Random Sampling and Sampling Distributions

120 hrs

1.1. Definition of random sample, parameter and statistics

1.2. Sampling distribution of the sample mean, proportion and sample variance (SRS with/without replacement)

1.3. Standard errors of sample mean and sample proportion

1.4. Concept of Central Limit Theorem (CLT) and its applications

1.5. Independence of sample mean and sample variance

1.6. Exact sampling distributions

Definition of central χ2, t and F and their properties

Inter-relation between the distributions

Application of χ2, t and F distributions in statistics

2. : Estimation

160 hrs

2.1. Point Estimation

Estimation of parameter, characteristic and properties of a good estimator (unbiasedness, consistency, efficiency, sufficiency)

Likelihood function and properties

Method of estimation: method of maximum likelihood estimation (Binomial, Poisson and Normal), method of minimum variance and method of moments and their properties

Cramer-Rao inequality

2.2. Interval Estimation

Confidence intervals of mean and difference of means

Confidence intervals for proportion and difference of proportions

Confidence interval for a difference between two means for paired data

Confidence interval estimate of correlation, regression coefficients and average value of dependent variable

Approximate prediction interval of dependent variable

Determination of sample size to estimate mean and proportion

Problem specific interpretation of confidence interval

3. Theory of Hypothesis Testing

8 hrs

3.1. Testing of hypothesis

Statistical hypothesis, simple and composite hypotheses, test of statistical hypothesis

Null and alternative hypotheses

Type I and type II errors

Level of significance, critical region, power of the test

One tailed and two tailed tests

Use of critical value and p-value approach in testing of hypothesis

Likelihood ratio test and its properties

Different scenario of using the concept of testing of hypothesis in data science related problems

4. Statistical Tests

120 hrs

4.1. Need and importance of statistical tests

4.2. Test of significance of mean (single and double samples, large and small samples, independent and dependent samples)

4.3. Test of significance of proportion (single and double samples)

4.4. Test significance of sample variance (Chi-square test)

4.5. Test significance of two sample variances

4.6. Overall fit of the regression model (F-test)

4.7. One way and two way Analysis of Variance (ANOVA)

4.8. Test of significance of correlation coefficient and regression coefficients

4.9. Assumptions for applying statistical tests

4.10. Applications of different statistical tests in data science related numerical problems

Laboratory Works

Title: Sampling distribution of mean and proportion, standard error and determination of sample size
Description: Number of practical problems: 1
Title: Confidence intervals of mean and difference of means. Confidence intervals for proportion and difference of proportions. Confidence interval for a difference between two means for paired data, confidence interval estimate of correlation, regression coefficients (interval estimation)
Description: Number of practical problems: 4
Title: Parametric test (covering most of the tests)
Description: Number of practical problems: 8
Title: Chi-square test
Description: Number of practical problems: 2

Reference Books

1.Bruce Peter and Bruce Andrew (2017). Practical Statistics for Data Scientists, O'Reilly Media, Inc.
2.Gupta S. C. and Kapoor V. K. (2007). Fundamentals of Mathematical Statistics, Sultan Chand and Sons, India
3.Hogg Robert V. McKean Joseph W. and Criag Allen T.(2019). Introduction to mathematical statistics, 8th edition, Pearson Education Inc.
4.Mayer, P. L. (1970). Introductory Probability and Statistical Applications, second edition Oxford and IBH Publishing Co. Pvt Ltd, New Delhi
5.Nitis Mukhopadhyay (2000). Probability and Statistical Inference, CRC Press Taylor & Francis Group.
6.Rohatgi, V. K. (1984). Statistical Inference, Wiley, New York.

Notes:

This syllabus follows the official Bachelor in Data Science curriculum of Tribhuvan University. In case of any doubt or revision, the university's published syllabus shall be considered authoritative.

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