1. A Quick Review

2. What are the conditions to construct CI for proportion?

3. The Large-Sample Confidence Interval for p
1. p is the sample proportion from a random sample
3. the sample size is small relative to the population size
2. the sample size n is large

4. Common Confidence Levels
Z-Critical

5. What is
Formula for the CI of P?
Standard Error?
Margin of Error?

6. Estimate of the standard deviation of p or standard error
The general formula for a confidence interval for a population proportion p is
Estimate of the standard deviation of p or standard error
The standard error of a statistic is the estimated standard deviation of the statistic.
point estimate

7. This is called the bound on the error estimation.
This is also called the margin of error.

8. The point estimate is
Example-
The article “How Well Are U.S. Colleges Run?” (USA Today, February 17, ) describes a survey of 1031 adult Americans. The survey was carried out by the National Center for Public Policy and the sample was selected in a way that makes it reasonable to regard the sample as representative of adult Americans. Of those surveyed, 567 indicated that they believe a college education is essential for success.

9. What is a 95% confidence interval for the
What is a 95% confidence interval for the population proportion of adult Americans who believe that a college education is essential for success?
Before computing the confidence interval, we need to verify the conditions.

10. Conditions:
2) The sample size of n = 1031 is much smaller than 10% of the population size (adult Americans).
3) The sample was selected in a way designed to produce a representative sample. So we can regard the sample as a random sample from the population.
1) np = 1031(.55) = 567 and n(1-p) = 1031(.45) = 364, since both of these are greater than 10, the sample size is large enough to proceed.
All our conditions are verified so it is safe to proceed with the calculation of the confidence interval.

11. What does this interval mean in the context of this problem?
Calculation:
Conclusion:
We are 95% confident that the population proportion of adult Americans who believe that a college education is essential for success is between 52.1% and 57.9%
What does this interval mean in the context of this problem?

12. Comment on certainty Vs Precision?
Compute a 90% confidence interval for this proportion.
Compute a 95% confidence interval for this proportion.
Compute a 99% confidence interval for this proportion.
What do you notice about the relationship between the confidence level of an interval and the width of the interval?
Comment on certainty Vs Precision?

14. What value should be used for the unknown value p?
Choosing a Sample Size
The bound on error estimation for a 95% confidence interval is
If we solve this for n . . .
Sometimes, it is feasible to perform a preliminary study to estimate the value for p.
In other cases, prior knowledge may suggest a reasonable estimate for p.
If there is no prior knowledge and a preliminary study is not feasible, then the conservative estimate for p is 0.5.
What value should be used for the unknown value p?
Before collecting any data, an investigator may wish to determine a sample size needed to achieve a certain bound on error estimation.

15. Why is the conservative estimate for p = 0.5?
.1(.9) = .09
.2(.8) = .16
.3(.7) = .21
.4(.6) = .24
.5(.5) = .25
By using .5 for p, we are using the largest value for p(1 – p) in our calculations.

16. In spite of the potential safety hazards, some people would like to have an internet connection in their cars. Determine the sample size required to estimate the proportion of adult Chinese who would like an internet connection in their cars to within 0.03 with 95% confidence.
What value should be used for p?
This is the value for the bound on error estimate B.
Always round the sample size up to the next whole number.

17. Try Me: Sample Size Calculation
If a TV executive would like to find a 95% confidence interval estimate within 0.03 for the proportion of all households that watch “The empress of china and silent Separation
(武媚娘传奇 and 何以笙箫)”regularly. How large a sample is needed if a prior estimate for p was 0.15.

18. Try Me: revisited
Suppose a TV executive would like to find a 95% confidence interval estimate within 0.03 for the proportion of all households that watch “The empress china and silent Separation (武媚娘传奇 and 何以笙箫)” regularly. How large a sample is needed if we have no reasonable prior estimate for p.

20. Quick survey The pace of the lecture for this slide set was… Fast
About right
A little slow
Too slow