1. Sampling & Sampling Distributions
Sampling vs Census
Reasons for Taking a Sample:
Save Time
Save Money
Infinite Population
Destructive Testing
More Accurate
Sampling Error - Sample Does Not Reflect the Population by Random Chance.

2. Sampling Bias – Sample Does Not Reflect the Population because
Certain Elements of the Population have a Higher Chance
of Selection.
Literary Digest Poll – 1936
Roosevelt ,897
Landon 1,293,669
Bias of Non-Response
Taking a Random Sample will Prevent Sampling Bias.
Simple Random Sample – Each Element of the Population has equal Chance of Selection.

3. Ex: Simple Random Sample
Select 3 people from 8 people
Mary
Joni
Neil
Don
Linda
Paul
Mark
Jane
Random Number Table

4. Modifications of Simple Random Sampling:
Systematic Random Sample – A Few Random Selections Force the
other Selections
Stratified Random Sample – Divide Population into Strata
Cluster Sampling – Divide Population into Clusters (Areas)

5. Sampling Distribution for Sample Mean
Ex: Population X | µ = 3
P(X) | 1/5 1/5 1/5 1/5 1/ σ2 = 2
Sample 2 Rolls from this Population:
{1,1} {2,1} {3,1} {4,1} {5,1}
{1,2} {2,2} {3,2} {4,2} {5,2}
{1,3} {2,3} {3,3} {4,3} {5,3}
{1,4} {2,4} {3,4} {4,4} {5,4}
{1,5} {2,5} {3,5} {4,5} {5,5}
Find the Sample Mean for these Samples

6. Sample Mean Distribution:
X | P(X) X•P(X) (X-µ) (X-µ)2 (X-µ)2•P(X)
| 1/25
1.5 | 2/25
| 3/25
2.5 | 4/25
| 5/25
3.5 | 4/25
4.5 | 2/25
5 | 1/25

7. Central Limit Theorem – The Distribution for the Sample Mean, X, is
Approximately Normal for a Large Enough Sample Size (n ≥30),
And and

8. Z Formula for Sample Mean Transformation to Standardized Normal Curve
Ex: Male Heights are Normally Distributed with a Mean of 70” Std Dev of 3”
P(X > 72”) = If n = 4, P( > 72”) =

9. n =25 P( > 72)

11. Sampling from a Finite Population
Finite Correction Factor
Modified Z Formula
Use If n > .05•N