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7/28/2019 Statistics for M.phil Education

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Program : M.Phil Education/ MS-Library InformationSciences

Course Name: Applied Statistics in Education & Library Sciences

Course Objectives

This course aims at introducing the students to business mathematics

and build up a sound foundation for studying the higher mathematical subjectof quantitative techniques and operational research. The course will be avaluable guide to business students who will be supposed to apply the modernmathematical techniques to solve a number of basic decision-makingproblems which they will encounter in their daily business transactions.Throughout the course the basic mathematical principles are explained,illustrated and applied in solving different financial and other related businessproblems with suitable examples.

Module No 1.

INTRODUCTION

Meaning of

Statistics

Characteristics ofStatistics

Descriptive and

inferential

statistics

Populations andsamples

Importance of

statistics

Observations

and variables

Variables

Discrete andcontinuous

variables Errors of

measurement

Significant digits

Rounding off a

number

Collection of

Data

Collection ofprimary data

Collection ofsecondary data

Editing of Data

PRESENTATION OF DATA

Introduction

Classification

Aims of

classification

Basic principlesof classification

Tabulation

Types of Tables Main parts of a

table and

construction

Frequency

Distribution

Class-Limits

Class-boundaries

Class-Mark

Class width or

interval

Constructing agrouped

Frequency

Distribution

Cumulative

frequencydistribution

Graphical

Representation

Frequency

polygon

Frequency Curve Cumulative

Frequency

polygon or Ogive

Ogive for

Discrete curves


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MEASURES OF CENTRAL TENDENCY OR AVERAGES

Introduction

Criteria of a

satisfactory

Average Types of

Averages

The Arithmeticmean

Mean from

Grouped data

Change of origin

and scale The Geometric

mean

The harmonicmean

The median

Quantiles

The mode

Empirical relationbetween mean

median and mode

TIME SERIES ANALYSIS

Introduction

Components of atime series

Secular trend Seasonal

variations

Cyclical

fluctuations

Irregular or

random variations Time series

decomposition

Analysis the

secular trend

The method of

freshand curve

The method of

semi-averages The method of

moving Averages

The method of

least-squares

Module No 2.

Sampling Distribution Sampling Distribution of the

mean Central Limit Theorem

Sampling Distribution of

Difference between Means.

Sampling Distribution of a

Sample Proportion

Sampling Distribution of

Difference between Proportions. Estimates and Estimators

Point Estimation

Criteria for Good point Estimators

Pooled Estimators from two or

more

Samples

Estimation by Confidence Interval

Confidence Interval Estimate of a

Population Mean

Interpretation of a Confidenceinterval Confidence Interval for

Difference of Mean

Confidence Interval for

Population Proportion

Confidence Interval for the

Difference between Proportions

One-Sided confidence IntervalSample size for Estimating

Population Mean

Sample size for Estimating

Population

Proportion Exercises.

Hypotheses


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Null and Alternative Hypotheses

Simple and Composite

Hypotheses

Test-Statistic

Acceptance and Rejection

Regions Type I and Type II Errors

The Power of a Test

The significance

One-Tailed and Two-tailed Tests

Sample size when a and B are

specified

Formulation of Hypotheses

General Procedure for Testing

Hypotheses

Tests Based on NormalDistribution

Testing Hypothesis about Mean of

a Normal Population when is

Known


a Non-Normal Population when

sample size is large

Testing Hypotheses about

difference between Two

population Means Testing Hypotheses about a

population Proportion when

sample size is large

Testing Hypothesis about

Difference between Twoproportion

Testing Hypotheses about

standard Deviation Large Samples

Relationship between Confidence

Interval and tests of Hypotheses.

The Students t-distribution

Properties of Students t-

distribution

The t-tables Distribution of Difference of

Sample Means: Small Samples

and 1=2

Assumptions in Using t-

distribution

Confidence interval Estimates o

Means From Small Sample.

Small Sample Tests of Means


a Normal population when isunknown and n


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Confidence interval Estimate of a,

the intercept of regression line.

Confidence interval Estimate of

mean value for a given value

of X.

Prediction interval of anindividual y value for a given

value of X.

Hypothesis testing in the

regression model

Testing hypothesis about B, the

population regression coefficient

Testing Hypothesis about a, the

intercept of population regression

Testing hypothesis about mean

value Testing hypothesis about

population variance

Testing hypothesis about Equality

of regression coefficient of two

regression lines

Testing hypothesis about the

linearity of regression

Confidence interval Estimatefor population correlation

coefficient

Hypothesis testing about

correlation coefficient

Testing the hypothesis that p=p0

(0)

Testing hypothesis about equality

of two correlations

Testing hypothesis about p=0 Testing hypothesis about the

equality of several correlations

Recommended Books

1. MATHEMATICS FOR BUSINESS AND ECONOMICS --- Robert H.Nicholson.

2. BUSINESS MATHEMATICS Mirza & Mirza 3rd Edition (1995):Farooq Kitab Ghar Karachi.

3. STATISTICAL THEORY PART-I -- Sher Mohammad Chaudhry,