Concept of Sampling

Concept of Sampling

›Introduction

Statistical analysis – Data Analyzing

Collection of Data

›Census Method

›Sample Method

Universe or population

Sample

Average and variance of sample = Sample statistic

Such values of population is parameters (µ , б)

Census Method

›Information collected from each and every unit of population

›Also called as Complete Enumeration Method

›Merits

›Reliable and accurate data

›Extensive Information

›Suitability

›Demerits

›More expensive

›More time consuming

›More labor required

›Not suitable for Specific Problem

›Sampling Method

›Data is collected from the sample of items selected from population

›Merits

›Saving time and money

›Intensive study

›Organizational Convenience

›More reliable results

›More scientific

›Demerits

›Less accurate

›Wrong conclusion

›Less reliable

›Not suitable

›Difference between Census and Sampling

Census

›All Items

›Expensive time ,money and labor

›Investigation with limited field

›Heterogeneous

›Each and every unit

Sampling

›Few items

›Economical

›Investigation with large field

›Homogenous

›Few unit

›Sampling Method

›Probability Sampling Method

›Simple random sampling

›Lottery method

›Tables of random numbers

›Merits

›Free from personal bias

›Equal chance of being selected

›Save time , labor and money

›Demerits

›Sample size is small , then sample is not adequately

›Universe small , not suitable

›Stratified Random sampling

›Heterogeneous

›Different strata acc to characteristics

›Merits

›More likelihood of representation of unit

›Comparative study

›More accuracy

›Demerits

›Limited scope

›Possibility of prejudice

›Systematic random sampling

›Systematically arranged and numbered

›Sample unit , equal interval

›Merits

›Simple method

›Little time

›Demerits

›Each unit doesn’t stand equal chance

›Multistage Random sampling

›Many stages

›Merits

›Regional basis

›Decision on the basis of sample alone

›Demerits

›Lot of time and labor

›Cluster Sampling

›Applied in pharmaceutical industry

›Non - Probability Sampling Method

›Judgment sampling

›Merits

›Less expensive

›Simple and easy

›Demerits

›Greater chance of prejudice

›Not very accurate and reliable

›Quota Sampling

›Merits

›Greater chance important unit being included

›Inquiry is more organized

›Convenience Sampling

›Extensive sampling

›Merits of Sampling

›Less time

›Less cost

›More reliable

›Mors detailed information

›Demerits

›Inaccurate and misleading

›Absence of qualified staff

›Sampling and Non Sampling Errors

›Error = Difference between Sample static and Population parameter

›Sampling errors = error arising due to drawing interferences about the population on the basis of few observation

›Two types of error

›Sampling error

›Non sampling error

›Errors may be occur in the collection , processing and analyzing of data

›Sampling Errors

›Biased errors

›Unbiased errors

›Faulty selection of the sampling method

›Faulty demarcation(Boundaries) of sampling unit

›Variability of the population which has different characteristic

›Bias in analysis

›Method of reducing Sampling errors

›Sample size – larger – less error

›Non Sampling Errors

›Faulty planning

›Faulty selection of the sample unit

›Lack of trained and experienced staff

›Errors in compilation

›Errors due to wrong statistical measures

›Framing of a wrong questionnaire

›Incomplete investigation of the sample survey

›Principle of Sampling

›Principle of Statistical Regularity

›According to king this law states that a moderately large number of items chosen at random from a large group are almost sure on the average possess the characteristic of large group

›Principle of Inertia of Large number

›Corollary of the principle of Statistical regularity

›Larger the size of the sample , more accurate result likely to be.

›Estimation of parameters

›Statistical inference is the estimation of population parameters from the corresponding sample static

›Statistical estimation

›It is the procedure of using a sample statistic to estimate a population parameter.

›Statistic used to estimate a parameter is called estimator

›Value taken by the estimator is called an estimate

›SE can be divided in two

›Point estimation and interval estimation

›Estimation of parameters

›Properties of good estimator

›Unbiasedness

›Average of the sample values = population parameter

›Estimator is unbiased = expected value of estimator = population

›Consistency

›Sample size increases and decrease in error

›Efficiency

›Variance of estimator is small , the distribution of estimator will be better in that its value is closer to Parameter value

›Sufficiency

›Sir R.A. Fisher

›A sufficient estimator is one that uses all information about the population parameter contained in the sample

›Test of Hypothesis

›It is an assumption about the population parameter to be tested based on sample information

›Hypothesis testing for making decision

›In attempting to reach decision , it is useful to make assumptions or guesses about the populations involved. Such assumption , which mat or may not be true are called statistical hypothesis

›Test of Hypothesis

›Procedure of hypothesis testing

›Set up the hypothesis

›Null hypothesis denoted by H0

› Alternate hypothesis by H1

›Set up the suitable significance level

› Determination of a suitable test statistic

›Test statistic = sample statistic – hypothesized PP

› Standard error of SS

›Determine the critical region

›Doing computation

›Making decision

›Type 1 and type 11 errors

›The hypothesis is true but our test rejects it

›The hypothesis is false but our test Accepts it

›The hypothesis is true but our test accepts it

›The hypothesis is false but our test rejects it

›One tailed and two-tailed test

›One tailed and two-tailed test

›Central limit theorem

›It is widely used in the field of estimation and inference. This states that if we select random sample of large size n from any population with mean and SD and compute the mean of each sample , then sampling distribution of mean approaches normal distribution with mean and SD б/√n. This is true even if population itself is not normal.

Statistical Quality Control

Introduction

• Growing competition
• Watch over quality
• Mass production unable to check the quality at each and every level
• SQC refers to use of statistical techniques in controlling the quality of manufacturing goods

Definition

• SQC should be viewed as a kit of tools which may influence decision to the function of specification , production or inspection
• An economic and effective system of maintaining and improving the quality of outputs throughout the whole operating process of specif. , prod. & insp. Based on continuous testing with random samples

Characteristic

• Control quality standard
• Exercise during production process
• Determine the variation
• Statistical charts

Advantages

• Quality under control or not
• Eliminate assignable causes
• Lower inspection cost
• Protect interest of consumer
• Healthy influence on the psychology of workers
• Earn the goodwill
• Guide for new plant

Causes & Methods

Causes of variation

• Assignable causes
• Chance causes

Methods of SQC

• Process control
• Product control

Acceptance Sampling

Acceptance sampling is concerned with the decision to accept a mass of non – conforming the quality. The decision is reached through sampling

Risks

How to conduct Acceptance sampling or Types of sampling Inspection Plan

1. Single Sampling Plan
2. Double Sampling Plan
3. Multiple Sampling Plan

Operating Characteristic Curve (OC Curve)

• Graphic measure of assessing the ability of sampling plan in distinguishing between good and bad items
• Depicts the relationship between the probability of acceptance the lot for different lot quality expressed in terms of percentage defectives

Control Charts

• +3Sigma Upper Control Limit
• Central Control Limit
• -3Sigma Lower Control Limit

Purpose & uses of control charts

• Determining the quality standards
• Detecting assignable & Chance Variation
• Reveals variation from desired level
• Necessary steps for correction
• simple to construct & easy to interpret
• Less inspection cost

Types of control charts

• On the basis of Variables

1. Mean Chart
2. Range Chart
3. SD Chart

• On the Basis of Attributes

1. p Chart (Fraction Chart)
2. np Chart (No of defects)
3. C Chart (No of defects per unit)

Marginal Costing &Break Even Analysis
Marginal Cost & Marginal Costing
Acc to ICMA
Marginal cost represents "the amount of any given volume of output by which aggregates costs are changed if the volume of output is increased by one unit"
In practice it is measured by total variable cost attribute to one unit
Marginal Cost & Marginal Costing
Acc to Blocker & weltmore
"marginal cost is the increase or decrease in total cost which results from producing or selling additional or fewer unit of product or from a change in the method of production or distribution such as the use of improved machinery ,addition or exclusion of a product or territory"
Marginal Cost & Marginal Costing
ICMA
Marginal costing as " the ascertainment of marginal costs and of the effect on profit of changes in volume or type of output by differentiating between fixed & variable cost"
Marginal costing is also know as "variable costing"
Characteristics of marginal costing
Analysis & presentation
Classification of cost (fixed, variable, semi variable)
Variable cost are regarded as cost of product
Fixed cost is treated as period cost
Finished goods & work in progress are valued as marginal cost
Contribution = sales or SP – marginal cost of sales
Assumption of marginal costing
Variable cost remain constant per unit of output
SP per unit remain unchanged
Fixed cost remain unchanged

Contribution
It is difference between sales & variable cost or marginal cost
Excess of SP over variable cost per unit
Also know as contribution margin or gross margin

If SP = 20/-
Variable cost = 15/-
Fixed exp = 50000/-
Total no of unit sold 8000
C = 20-15 = 5
Total contribution = 8000*5 = 40000
Advantages
Fixing selling prices
Assist break even point
Suitable product mix
Alternative method of production
Purchase or manufacture
Adding new product
Marginal costing equation
Sales – variable cost = contribution
Sales = variable cost + contribution
Sales = variable cost + fixed cost + profit/loss
Sales – variable cost = fixed cost + profit/loss
S-V = F + P
Cost – Volume profit analysis
Studying the relationship between cost , volume & profits.
Cost of manufacture , volume of sales ,SP of product
In words of Herman C. Heiser
"the most significance single factor in profit planning of the average business is the relationship between the volume of business , cost & profits"
Break-Even Analysis
In two senses
Narrow senses
Broad senses
In broad sense break even analysis refers to the study of relationship between cost , volume , and profit at different levels of sales or production
In narrow sense it refers to a technique of determining that level of operation where total revenue equal total expenses no profit no loss point.
Assumptions
All element of cost
Variable cost remain constant per unit
Fixed cost remain constant
SP remain unchanged
Volume of factor is only influence cost
No change in general price level
Break even point
Point of sales volume at which total revenue is equal to total cost.
No profit no loss point
Total sales is equal to total cost
Also called as Critical point or Equilibrium point or balancing point
Managerial application of marginal costing
Pricing decision
Profit planning
Make or but decision
Selection of suitable sales mix
Effect of change in sales price
Alternative method of production
Optimum level of activity
Capital investment decision
Advantages of marginal costing
Simple to operate
Removes complexities
Help management in production planning
No possibility of fictitious profits
BEP calculation
Decision making
Helpful in cost control
Profit planning
Management reporting
Limitation
SP don’t remain constant
Ignores time factor

Budgeting & Budgetary Control
Introduction
Planning is basic managerial function
Achieving goal
Control is to check
Budget & Budgeting
Budget is monetary and quantitative expression of business plan & polices to be pursued in future time period
Budgeting is used for preparing budgets & other procedures for planning, coordinating and controlling of business enterprises

Budget & Budgeting
Acc to CIMA , Official terminal
"Budget is a financial and quantitative statement prepared prior to be defined period of time"

Budgetary Control
Process of determining various budgeted figures for the enterprises for the future period
then comparing the budgeted figures with the actual performance for calculating variance

Acc to J.Batty
"A system which uses budgets as a means of planning and controlling all aspect of producing and selling commodities and services"

Budgetary involves
Objects are set by preparing budgets
Business is divided into various responsibility centres
Actual figures are recorded
Comparison
Action
Budget , Budgeting , Budgetary control
Budget is a blue print expressed in quantitative term
Budgeting is technique for formulating budget
Budgetary control refers to principles , procedures and practice of achieving given objective through budgets
Objectives of budgetary control
Ensure planning for future
Co ordinate the activities
Operate various cost centres & departments
Elimination of wastage
Centralize the control system
Fixation of responsibilities of various individuals
Characteristics of Good Budgeting
Involve person at different level
Proper fixation of authority & responsibility
Target of budget should be realistic
Good system of accounting
Support of top management
Impart budgeting education


Elements of budget
Plan
Operations & Resources
Financial term
Specified future period
Coordination
Comprehensiveness (Master Budget)
Purpose of Budget
Explicit statement of expectation
Communication
Coordination
Expectation as a framework of judging performance
Advantages
Maximization of profits
Co-ordination
Specific aim
Tool of measuring performance
Determining weakness
Corrective action
Reduces cost
Introduction of incentives schemes
Limitation
Uncertain future
Revision required
Conflict among departments
Depends upon support of top management
Classification & Types
Classification according to time
Long term budgets
short term budgets
Current budgets
Classification on the basis of function
Operating budget
Financial budget
Master budget
Classification on the basis of flexibiltiy
Fixed budget
Flexible budget
Acc to time
Long term budgets
Between 5 to 10 years
Short term budget
1 to 2 years
Current budget
Months or weeks
On basis of function
Operating budget
Sales budget , production budget , purchase budget , raw material budget ,
Financial budget
Cash budget , working capital budget , capital expenditure budget
Master Budget
On the basis of flexibilty
Fixed budget
Flexibility budget
Performance Budget
Budget based on functions , activities & projects.
The budgeting system in which input costs are related to the performance i.e. end result
System which provides appraisal & measures
Conventional budgets
"The performance budget is a budget based on function , activities and projects which focus attention on the accomplishments , the general and relative importance of the work to be done and the services to be rendered rather than upon the means of accomplishments such as personnel , service , supplies , equipments. Under this system the function of various org unit would be split into programmes of activities and estimated would be presented for each"
Establish relationship between inputs and their direct output
It involves
Developments of performance criteria for various programmes
Assessment of performance of each programme
Assessment of performance of each responsibility unit
Comparison of the actual performance with budget
Undertake periodic review
Zero Based budgeting
Latest technique of budgeting
First introduced in America in 1962
It starting from scratch
Normal technique use previous year cost level
Inefficiencies
Last year as a guide and what to be done
In zero based budgeting every year is taken as new year
Zero Based budgeting
Justified acc to present situation
Manager is to justify why he want to spend
Spending on various will depend upon their justification
Traditional budgeting Vs Zero based budgeting
Traditional
More accounting oriented then decision oriented
Monitoring toward expenditure
Inc. or Dec. in expenditure
Vertical communication
Zero base
Decision oriented
Towards achievement of objective
Cost benefit analysis
Vertical & horizontal communication
Process or steps
Objective of budgeting should be determined
Extent should be decided
Decision packages
Cost & benefit analysis
Selecting ,approving decision , finalising the budget
Benifits
Allocate funds
Efficiency of management
Identify wasteful & economical areas
Optimum use of resources
Evaluate the performance
Organizational goals
Limitations
Is not possible in non financial matters
Difficult in formulation & ranking of decision packages
Lot of time
Lot of cost