1. Course Outline Presentation Reference Course Outline for MTS-202 (Statistical Inference) Fall-2009 Dated: 27 th August 2009 Course Supervisor(s): Mr. Ahmed Raza, Ms. Aniqa Kashif and Yaseen Ahmed Meenai

2. Course Description This is the second course in Statistics. One of the primal aims of the course is to try to give a thorough insight and understanding of fundamental statistical concepts in the context of physical sciences & engineering, social & management sciences --- in particular economics and management problem-situations. The fundamental statistical tools & methodologies enable us to analyze a wide variety of quantitative and qualitative data collected in diverse problem-situations encountered in the real world. The purpose of the inferential statistics is to test, deduce and infer the validity of different types of hypotheses and models built on the basis of the raw data collected in diverse problem-situations. The course will also provide the opportunity to learn a few basic statistical softwares like SPSS, Minitab, MS-Excel and ISP. Starred Material (*) will be covered if time permits towards the end of the course. Prerequisites:- MTS102 Introduction to Statistics.

3. Grading Plan & Books:- Assignments 10 (Two assignment each carrying 5 marks will be given) Quizzes 10 (Three quizzes each carrying 5 marks will be given and Will consider the best of 2) 1 st Term Exam 20 2 nd Term Exam20 Final Exam 40 ------------------------------ Total 100 Text Book :- Author: Neil A. Weiss, Title: Introductory Statistics, Edition 5 th, Publisher Pearson Addison Wesley (Chapters 7-13, 15, 16) Reference Book:- Authors : Walpole & Myers (Eight Ed.); Probability & Statistics for Engg. & Scientists

4. Topics to be covered… [Remark: L stands for 75-minute lecture.] 1-Statistics Refresher:- What is Statistics? Descriptive and Inferential Statistics; Significance and application of Statistics; Introduction to key terms. The Normal Distribution, Use of Standard Normal table, 2-Sampling Distributions:- Sampling Distribution, Sampling error, mean and standard deviation of sampling distribution of sample means, central limit theorem, sampling distribution of sample proportions, Sampling distribution of difference between two sample means. [3L]

5. Topics to be covered… [Remark: L stands for 75-minute lecture.] 3-Estimation:- Concept of Estimate, Estimation and Estimator, Point and Interval Estimation. Estimating a Population Mean (For a Normal Population):- Point Estimate (M.L.E.), Interval Estimate (confidence interval for population mean when risk is known), margin of error, Determining sample size, (confidence interval for population mean when risk is unknown), properties of t-distribution, checking the assumption of normality. [3L]

6. Topics to be covered… [Remark: L stands for 75-minute lecture.] 4-Testing of Hypothesis:- Concept of Statistical Hypothesis, Null and Alternative Hypothesis, Type I and Type II errors with examples. Hypothesis Tests for single Population Mean:- Hypothesis Test for one population Mean when  is known, P-value approach, Hypothesis Test for one population Mean when  is unknown, Nonparametric Method, Wilcoxon Signed-Rank Test, Selection criteria for choosing a test (optional). [3L] (Some Case studies)

7. Topics to be covered… [Remark: L stands for 75-minute lecture.] 5-Hypothesis Tests for two Population Means:- Hypothesis tests for the difference between two population means using and when population variances assumed to be equal or unequal, Mann-Whitney Test, Inferences for two population means using paired samples, Paired Wilcoxon Signed-Rank Test (optional). [3L] 6-Inferences for the Population Proportions:- Sample and population proportions, Sampling distribution of sample proportion, Hypothesis tests for one population proportion, sampling distribution of the difference between two sample proportions, Confidence interval and Testing of hypothesis for difference between two population proportions. (Some Case Studies)[2L]

8. Topics to be covered… [Remark: L stands for 75-minute lecture.] 7-Inferences for Population Standard Deviations:- Chi- Square Distribution and its properties, Confidence interval and Hypothesis test for a population Standard Deviation, The f-distribution and its properties, Confidence interval and Hypothesis tests for two population standard deviations. More Chi-Square Procedures- Chi-Square distribution and its properties, Goodness-of- Fit Test, Contingency Tables, Independence Test. [3L] (Some Case Studies)

9. Topics to be covered… [Remark: L stands for 75-minute lecture.] 8-Analysis of Variance and Experimental Design:- One-Way Analysis of variance, Assumptions for the One-Way Analysis of Variance, Test concerning the equality of several population means, Tukey Multiple comparison, Two-Way Analysis of variance, Concept of Experimental Design, Completely Randomized Design, Randomized Block Design and their analysis. [3L] (Some Case Studies)

10. Topics to be covered… [Remark: L stands for 75-minute lecture.] 9-Inferential Methods in Regression and Correlation:- The linear regression model and its assumptions, Analysis of Residuals, Confidence Interval and Hypothesis tests for the slope of the population regression line, Estimation and Prediction, Prediction Intervals, Confidence interval and Test concerning population correlation coefficient. [3L] Multiple Regression Analysis (*):- Concept of multiple regression, Estimation of regression parameters, inferences concerning this model, checking model assumptions and residual analysis, polynomial regression, Multicollinearity. [2L] (Some Case Studies) (*) Subjected to The Availability of Time Some Sessions in Computer Lab:- These sessions would be based on some course related problems using MS- Excel and MINITAB (the statistical package)