STAT 110 - Section 5
Lecture 6
Professor Hao Wang
University of South Carolina
Spring 2012
Last time
Population and Sample
(II) Sample variability
Example
How many hours of sleep does an average USC
undergrad have ? Ask your 2 neighbors and
average their answers.
A
B
C
D
E
less than 5 hrs
5-6
7-8
9-10
more than 10 hrs
Population ?
Parameter ? Sample ? Statistic ?
Example
How many hours of sleep does an average USC
undergrad have ? Ask your 5 neighbors and
average their answers.
A
B
C
D
E
less than 5 hrs
5-6
7-8
9-10
more than 10 hrs
Population ?
Parameter ? Sample ? Statistic ?
Sampling Variability
bias – consistent, repeated deviation of the sample
statistic from the population parameter in the
same direction when we take many samples
 systematically misses in the same direction
variability – describes how spread out the values of
the sample statistic are when we take many
samples.
 amount of scattering
Picturing Bias and Variability
Variability of
1,000 of size n = 100
Variability of
1,000 of size n = 1,523
Notice that with larger samples (1523 vs. 100), there is a lot less variability….but
the distribution is still centered at p = 0.60 (so p-hat is unbiased for p)
Example: 2012 Florida Republican
Primary
http://www.rasmussenreports.com/public_con
tent/politics/elections/election_2012/election
_2012_presidential_election/florida/2012_flo
rida_republican_primary
10
In the previous poll:
A – The population is the 750 voters
B – The population is all likely Florida voters
In the previous poll:
A – The percent of all likely FL voters favoring
Gingrich is the Parameter and the 41% of the
750 is the statistic
B – The percent of all likely FL voters favoring
Gingrich is the statistic and the 41% of the 750
is the parameter
In the previous poll:
A – The variability is because Gingrich has
been in the news a lot recently, and the bias is
because it was a random sample.
B – The variability is because it was a random
sample, and the bias is because Gingrich has
been in the news a lot recently.
(III) Margin of Error
Margin of Error
During the week of 8/10/01, CNN conducted a poll
asking an SRS of 1000 Americans whether they
approve of President Bush's performance as
President. The approval rating was 57% (plus or
minus 3%). In their next poll conducted during the
week of 9/21/01, CNN conducted the same poll
asking an SRS of 1000 Americans whether they
approve of President Bush's performance as
President. The approval rating was 90% (plus or
minus 3%).
Why the difference in ratings?
Where does plus or minus 3% come from?
Margin of Error
The margin of error (MOE) is a value that
quantifies the uncertainty in our estimate.
When using the sample proportion to
estimate the population proportion, the
MOE is a measure of how close we
believe the sample proportion is to the
population proportion.
Calculating Margin of Error
Use the sample proportion
from a SRS of
size n to estimate an unknown population
proportion p.
For 95% confidence (the quick formula):
Example: Margin of Error
The CNN Poll interviewed 1000 people. What is
the margin of error for 95% confidence (using
the quick formula)?
Answer: Recall 95% confidence
Example: Margin of Error
If the sample size is 100, what is the margin of error for
95% confidence (using the quick formula)?
A.0.10%
B.0.01%
C.10%