### Introduction to Statistics (URAC-5108) (BS-3rd)

This is an introductory course in statistics designed to provide students with the basic concepts of data analysis and statistical computing. Topics covered include basic descriptive measures, measures of association, probability theory, confidence intervals, and hypothesis testing. The main objective is to provide students with pragmatic tools for assessing statistical claims and conducting their own statistical analyses. Statistics is the art of using data to make numerical conjectures about problems. Descriptive statistics is the art of summarizing data. Topics include histograms, the average, the standard deviation, the normal curve, correlation. Statistical reasoning depends on the theory of probability. Topics include chance models, expected value, standard error, probability histograms and convergence to the normal curve. Statistical inference is the art of making valid generalisations from samples. Topics include estimation, measurement error and tests of statistical significance

Course Objectives.

1. Providing students with a formal treatment descriptive and inferential statistics.
2. To introduce the students to the fundamentals of probability and probability distributions, sampling and sampling distributions, hypothesis testing, regression and correlation illustrate these concepts with applications.
3. Fostering understanding through real-world statistical applications.

Learning outcomes

At the end of the course, students will be able to:

• Display data graphically and interpret graphs: stem and leaf plots, histograms, and box plots.
• Recognize, describe, and calculate the measures of location of data: quartiles and percentiles.
• Recognize, describe, and calculate the measures of the center of data: mean, median, and mode.
• Recognize, describe, and calculate the measures of the spread of data: variance, standard deviation, and range.
• Recognize and differentiate between key terms.
• Apply various types of sampling methods to data collection.
• Create and interpret frequency tables.
• Understand and use the terminology of probability.
• Determine whether two events are mutually exclusive and whether two events are independent.
• Calculate probabilities using the Addition Rules and Multiplication Rules.
• Construct and interpret Venn Diagrams.
• Recognize and understand discrete probability distribution functions.
• Calculate and interpret expected values.
• Recognize the discrete and continuous probability distributions.
• Interpret the Student’s t probability distribution as the sample size changes.
• Discriminate between problems applying the normal and the Student’s t distributions.
• Calculate the sample size required to estimate a population mean and a population proportion given a desired confidence level and margin of error.
• Differentiate between Type I and Type II Errors
• Conduct and interpret hypothesis tests for a one and two-population mean, population standard deviation known.
• Discuss basic ideas of linear regression and correlation.
• Calculate and interpret the correlation coefficient.
• Use interpolation and extrapolation.
• Understand the concept of multiple linear regression models

Contents

Unit 1. What is Statistics? Definition of Statistics, Population, sample Descriptive and inferential Statistics, Observations, Data, Discrete and continuous variables, Errors of measurement, Significant digits, Rounding of a Number, Collection of primary and secondary data, Sources, Editing of Data. Exercises.

Unit 2. Presentation of Data: Introduction, basic principles of classification and Tabulation, Constructing of a frequency distribution, Relative and Cumulative frequency distribution, Diagrams, Graphs and their Construction, Bar charts, Pie chart, Histogram, Frequency polygon and Frequency curve, Cumulative Frequency Polygon or Ogive, Historigram, Ogive for Discrete Variable. Types of frequency curves. Exercises.

Unit 3. Measures of Central Tendency: Introduction, Different types of Averages, Quantiles, The Mode, Empirical Relation between Mean, Median and mode, Relative Merits and Demerits of various Averages. properties of Good Average, Box and Whisker Plot, Stem and Leaf Display, definition of outliers and their detection. Exercises.

Unit 4. Measures of Dispersion: Introduction, Absolute and relative measures, Range, The semi-Inter-quartile Range, The Mean Deviation, The Variance and standard deviation, Change of origin and scale, Interpretation of the standard Deviation, Coefficient of variation, Properties of variance and standard Deviation, Standardized variables, Moments and Moments ratios. Exercises.

Unit 5. Probability and Probability Distributions: Discrete and continuous distributions: Binomial, Poisson and Normal Distribution. Exercises.

Unit 6. Sampling and Sampling Distributions: Introduction, sample design and sampling frame, bias, sampling and non sampling errors, sampling with and without replacement, probability and nonprobability sampling, Sampling distributions for single mean and proportion, Difference of means and proportions. Exercises.

Unit 7. Hypothesis Testing: Introduction, Statistical problem, null and alternative hypothesis, Type-I and Type-II errors, level of significance, Test statistics, acceptance and rejection regions, general procedure for testing of hypothesis. Exercises.

Unit 8. Testing of Hypothesis- Single Population: Introduction, Testing of hypothesis and confidence interval about the population mean and proportion for small and large samples, Exercises.

Unit 9.Testing of Hypotheses-Two or more Populations: Introduction, Testing of hypothesis and confidence intervals about the difference of population means and proportions for small and large samples, Analysis of Variance and ANOVA Table. Exercises.

Unit 10. Testing of Hypothesis-Independence of Attributes: Introduction, Contingency Tables, Testing of hypothesis about the Independence of attributes. Exercises.

Unit 11. Regression and Correlation: Introduction, cause and effect relationships, examples, simple linear regression, estimation of parameters and their interpretation.  r and R2. Correlation. Coefficient of linear correlation, its estimation and interpretation.  Multiple regression and interpretation of its parameters. Examples

Recommended Books

1. Walpole, R. E, (1982) “Introduction to Statistics”, 3rd Ed., Macmillan Publishing Co., Inc. New York.
2. Muhammad, F, (2005) “Statistical Methods and Data Analysis”, Kitab Markaz, Bhawana Bazar Faisalabad.

Suggested Books

1. Walpole, R. E., & Myers, R. H. (2012). Probability & statistics for engineers & scientists. Pearson Education Limited.
2. Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2016). Statistics for business & economics. Nelson Education.

Assesment Criteria

• Sessional: 20 (Assignment 10, Attendance 05, Quiz 05)
• Mid-Term Exam: 30
• Final-Term Exam: 50

Time Table

 Day Time Wednesday 11:00 to 12:00 pm Thursday 11:00 to 12:00 pm Friday 11:00 to 12:00 pm

Commencement of Classes                                                   October 12, 2020

Mid Term Examination                                                            December 14-18, 2020

Final Term Examination                                                          February 08-12, 2021

Declaration of Result                                                              February 19, 2021