The Central Limit Theorem

1
Moral Values Gallup Personal Interviews 1000
adults per countryFebruary - May 1997
Do you think it is, or is not, morally wrong for
a couple to have a baby if they are not married?
2
Margin of Error as a Function of x/n
a 0.05 n 1,000
Margin of Error
x/n
3
Proportions Choosing a Sample Size
E is the desired margin of error, before
the sample is selected.
Problem Desired sample size depends on x/n, an
unknown.
4
Margin of Error as a Function of n and x/n
a 0.05
n 250
n 500
n 1000
Margin of Error
x/n
5
A 100(1-a) Confidence Interval for m
s known
n ? 30
s unknown
s known
population normal
n lt 30
s unknown
?
population not normal
AVOID!
6
Normal Population
Case 1 s is known.
Confidence Interval Limits

Z
s/ n
Case 2 s is unknown.

tn-1
s/ n
If n ³ 30, tn-1 Z.
7
The Role of the Population Size
SAMPLING
with replacement
without replacement
Finite Population Correction
8
Finite Population Correction Factor
Means
estimate with
estimate with
9
CI How You Ask
Three ways of asking for 80 intervals
Range I am 80 sure that the price of this car
is between ___ and ___.
2-point I am 90 sure the price of this car is
greater than ___. I am 90 sure the price of this
car is less than ___.
3-point adds one more question. I think the
price of this car is as likely to be above this
price as below it ___.
10
Conclusion

• This week Estimation
• What is a good value for m or for p?
• Next week Hypothesis Testing
• Test to see if our preconceived ideas about m
  or p are correct or not