1. Confidence Intervals & Polls
Lesson 7

2. Estimating m Sample mean is a point estimate of m Single value
SE as a measure of fit
Confidence intervals
Boundaries for true value of m
95% most common; 99% also used
Based on
z or t
Mean & standard error ~

3. Computing Confidence Intervals
When s is known
Mainly for standardized variables
e.g., IQ, ACT, SAT, GRE
General formula
Use z scores that at boundaries of desired interval

4. 95% Confidence Intervals for IQ
Sample from population of IQ scores
z = ~

5. 95% Confidence Intervals for IQ
Lower boundary
Upper boundary or
How does interval change if n=25?
Wider or narrower?
Why? What does it mean? ~

6. Changing the Confidence Level
99% confidence interval
z =
How does interval change? ~
Lower boundary
Upper boundary

7. Meaning of Confidence Interval
E.g., 95% confidence interval
If we compute confidence intervals for 100 samples
95 would contain true value of m
5 would not
No way to know which group any single confidence interval falls in
Always some probability it does not
P (error) = .05 ~

8. Confidence Intervals: When s unknown
Same general procedure & formula
Differences
Must use s instead of s
Introduces more uncertainty (error)
Use estimated standard error
Use t instead of z
df important ~

9. The t distribution 95% confidence intervals
More uncertainty  need wider intervals
t distribution
Adjusts based on sample size
df = n-1
Very large samples: t ≈ z
Smaller samples: t > z
Critical values of the t-distribution
A.2, pg 803 ~

10. The t distribution To find t, need… df = n-1 Confidence level
Actually area in tails (1-p)
Use Two-tailed Test column
Law of large numbers
As n 
Uncertainty  ~

11. Computing confidence Intervals with t
s is unknown
Need
t value
df = n-1; 1-p
Estimated standard error ~

12. 99% Confidence Interval: s unknown
Mean number hours spent studying for a psychology course? ~

13. 99% Confidence Interval: s unknown
Lower boundary
Upper boundary or
How does interval change if…
Smaller or larger sample?
95% confidence level? ~

14. Opinion Polls & Confidence Intervals
Opinion polls ubiquitous
Politics, public policy, consumer products, etc.
Often misrepresented / misinterpreted
Poll results reported as
Proportion & margin of error
Actually reporting confidence interval ~

15. Opinion Polls in the News
Give example of poll
Changes from week to week
Can we say things are really changing?

16. Opinion Polls & Confidence Intervals
Our example: Binomial data
only 2 possible responses
Yes/no; Candidate A or Candidate B
Proportions
Proportion choosing a response
Parameter: P, statistic: p
All responses: p + (1-p)
Margin of error ~

17. Computing Margin of Error
Confidence interval formula
Computing standard error of proportion
Rest of computation same as before ~

18. Example: Election Opinion Poll
250 voters asked if they will vote for…
Jane Jones (55%)
John Smith (45%)
At 95% confidence level
What is margin of error?
Can we say Ms. Jones will win? ~

19. Example: Computing Margin of Error
Compute standard error
Compute margin of error

20. Example: 95% Confidence Intervals
Jane Jones
John Smith
If Smith wins were polls wrong?
No, within margin of error. ~

21. A Guide for Interpreting Polls
Who paid for poll and conducted it?
Do they have vested interest?
Are they reputable / capable?
How many participants & how chosen?
Random sample? Important subgroups?
Ability to give informed answers?
e.g., 1st graders on national elections?
Opinions represent only group actually polled
e.g., college-age views may not be representative of all adults ~
Adapted from article by Ken Blake, PhD, MTSU School of Journalism

22. A Guide for Interpreting Polls
The wording & order of questions
Both can bias responses
The confidence level & margin of error
Margin of error must be recalculated if drawing conclusions about subgroups
What is the response rate?
Low rates  respondents may be very different from non-respondents ~
Adapted from article by Ken Blake, PhD, MTSU School of Journalism

23. Confidence Intervals Can be computed for many statistics
Formula for standard error changes
Related to hypothesis testing
Also alternative to it, along with meta-analysis
Covered in next lesson ~