Download Business Statistics: A Decision

Populations and Samples

A Population is the set of all items or individuals
of interest


Examples:
All likely voters in the next election
All parts produced today
All sales receipts for November
A Sample is a subset of the population

Examples:
1000 voters selected at random for interview
A few parts selected for destructive testing
Every 100th receipt selected for audit
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.
Chap 1-1
Sampling Techniques
Sampling
Probability/Statistical
Sampling
Nonprobability/
Nonstatistical
Sampling
Judgement
Simple
Random
Convenience
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.
Systematic
Stratified
Cluster
Chap 1-2
Nonprobability Sampling


Nonstatistical sampling  samples selected
using convenience, jugement, or other
nonchance prosesses.
Convenience sampling:

Samples selected from the population based
on accessibility or easy of selection.
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.
Chap 1-3
Probability Sampling

Items of the sample are chosen based on
known or calculable probabilities
Statistical/Probability
Sampling
Simple
Stratified
Systematic
Cluster
Random
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.
Chap 1-4
1. Simple Random Sampling

Every individual or item from the population has
an equal chance of being selected.

Selection may be with replacement or without
replacement.

Samples can be obtained from a table of
random numbers or computer random number
generators.
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.
Chap 1-5
1. Simple Random Sampling
Example:

There are 185 students  you will pick up only
5 students as samples. How do you choose the
samples ?
 Use the random number.
Random Numbers Table
1. Simple Random Sampling
START
1. Simple Random Sampling

How to use a random number table




Let's assume that we have a population of 185 students and each
student has been assigned a number from 1 to 185. Suppose we wish
to sample 5 students (although we would normally sample more, we
will use 5 for this example).
Since we have a population of 185 and 185 is a three digit number, we
need to use the first three digits of the numbers listed on the chart.
We close our eyes and randomly point to a spot on the chart. For this
example, we will assume that we selected 20631 in the first column.
We interpret that number as 206 (first three digits). Since we don't have
a member of our population with that number, we go to the next
number 899 (89990). Once again we don't have someone with that
number, so we continue at the top of the next column. As we work
down the column, we find that the first number to match our population
is 100 (actually 10005 on the chart). Student number 100 would be in
our sample. Continuing down the chart, we see that the other four
subjects in our sample would be students 049, 082, 153, and 164.
1. Simple Random Sampling

Microsoft Excel has a function to produce random numbers.

The function is simply:
=RAND()


Type that into a cell and it will produce a random number in that cell. Copy the
formula throughout a selection of cells and it will produce random numbers
between 0 and 1.
If you would like to modify the formula, you can obtain whatever range you wish.
For example, if you wanted random numbers from 1 to 250, you could enter the
following formula:
=INT(250*RAND())+1
The INT eliminates the digits after the decimal, the 250* creates the range to
be covered, and the +1 sets the lowest number in the range.
1. Simple Random Sampling
Example:
If you want to select 10 sample students from 100 students, you could type in a cell
the following formula:
=INT(100*RAND())+1
After that, a number (between 1 – 100) will appear then copy that formula to other
9 cells (below, up, right or left from the first cell). You can find the ten numbers
(between 1 – 100) which selected randomly as samples:
40
53
74
99
69
32
2
69
16
11
Number of students which chosen randomly as sample
2. Stratified Sampling

Population divided into subgroups (called strata)
according to some common characteristic

Simple random sample selected from each
subgroup

Samples from subgroups are combined into one
Population
Divided
into 4
strata
Sample
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.
Chap 1-12
3. Systematic Sampling

Decide on sample size: n

Divide frame of N individuals into groups of k
individuals: k=N/n

Randomly select one individual from the 1st
group

Select every kth individual thereafter
N = 64
n=8
First Group
k=8
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.
Chap 1-13
4. Cluster Sampling


Population is divided into several “clusters,”
each representative of the population
A simple random sample of clusters is selected

All items in the selected clusters can be used, or items can be
chosen from a cluster using another probability sampling
technique
Population
divided into
16 clusters.
Randomly selected
clusters for sample
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.
Chap 1-14
What Size Sample Is Needed?
Some principles :
1. The greater the dispersion or variance, the larger the
sample.
2. The greater precision of the estimate, the larger the
sample.
3. The narrower or smaller the error range, the larger
the sample.
4. The higher the confidence level, the larger the
sample.
5. The greater the number of subgroups of interest
within sample, the larger the sample.
6. The lower cost/respondent, the larger the sample.
Determining Sample Size

Formula:
where:
n = sample size
Zα/2 = 1.96 (from table of Z distribution, α = 0.05)
E = Margin Error (known)
σ = Standard deviation (known)
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.
Chap 1-16
Determining Sample Size
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc.
Chap 1-17