STAT 3120 Statistical Methods I

1
STAT 3120Statistical Methods I

• Lecture 2
• Confidence Intervals

2
STAT3120 - Confidence Intervals

• As you learned previously, Inferential Statistics
  relies on the Central Limit Theorem. Methods for
  making inferences are based on sound sampling
  methodology and fall into two categories
• Estimation Information from the sample can be
  used to estimate or predict the unknown mean of a
  population. Example What is the mean decrease
  in Cholesterol due to taking Drug A?
• Hypothesis Testing Information from the
  sample can be used to determine if a population
  mean is greater than or equal to another
  population or a specified number. Example Is
  the mean cholesterol reading for patients taking
  Drug A lower than the cholesterol reading for a
  control group?

3
STAT3120 - Confidence Intervals
The first category of inference estimation is
most commonly used to develop Confidence
Intervals. A Confidence Interval around a
population parameter is developed using
x ? z ?/2 (s/SQRT(n))
Where x sample mean z ?/2 the appropriate
two sided Z-score, based upon desired
confidence s sample standard deviation n
number of elements in sample
4
STAT3120 - Confidence Intervals
For example, lets say that we took a poll of 100
KSU students and determined that they spent an
average of 225 on books in a semester with a std
dev of 50. Report the 95 confidence interval
for the expenditure on books for ALL KSU
students.
5
STAT3120 - Confidence Intervals
Now, assuming that you need to maintain this MOE,
but at a 99 confidence, what is the new sample
size? You can do the algebra yourself, or use
the following transformation of the
formula n(z)2d2/E2 Where nsample size z
z-score associated with selected alpha d
standard deviation (of sample or population) E
Maximum Margin of Error/Width of interval
6
STAT3120 - Confidence Intervals
(From Page 201) What if I wanted to be 90
confident? What if I wanted to be 95
confident? What if I wanted to be 99 confident?
Typical Z scores used in CI Estimation 90
confidence 1.645 95 confidence 1.96 98
confidence 2.33 99 confidence 2.575
7
STAT3120 - Confidence Intervals
A Confidence Interval around a population
proportion is developed using
p ? z ?/2 SQRT((pq/n))
Where p sample proportion z ?/2 the
appropriate two sided Z-score, based upon desired
confidence q 1-p n number of elements in
sample
8
STAT3120 - Confidence Intervals
For example, lets say that we took a poll of 100
KSU students and determined that 26 voted
Libertarian. Report the 95 confidence interval
for the proportion of KSU students expected to
vote Libertarian.
9
STAT3120 - Confidence Intervals
Now, assuming that you need to maintain this MOE,
but at a 99 confidence, what is the new sample
size?
10
STAT3120 - Confidence Intervals
FUN SPSS AND SAS EXERCISES! ltUsing the Customer
Survey Datasetgt