1. SP 225 Lecture 11
Confidence Intervals

2. Three Separate Distributions
Sample distribution
Empirical and known
Intended to help learn about the population
Population distribution
Empirical and unknown
Properties estimated using statistics
Sampling distribution
Theoretical or non-empirical
Properties well-known and based on probabilities

3. Example Problem
A researcher has gathered information from a population with an average of 2.3 people and a standard deviation of If the researcher collects samples of 100 households, what proportion of samples will have a mean less that 2.25?

4. Confidence Interval
Mathematical statement that says that the parameter lies within a certain range of values
95% confident that the mean length of employment at XYZ automotive is between 8 and 12 years

5. Probability Distribution for Population Mean
95% confident that the mean length of employment at XYZ automotive is between 8 and 12 years
(sample)

6. Confidence Interval Example
A random sample of 100 television programs contained an average of 2.37 acts of physical violence per program. The standard deviation of the number of acts of violence on television in the population is 3. At the 99% level, what is your estimate of the mean number of acts of violence for all television programs?

7. Confidence Interval Formula

8. Confidence Interval Estimate

9. Confidence Interval Example 2
A researcher has gathered information from a random sample of 178 households. The households averaged 6.0 hours of television viewing per day with a standard deviation in the sample of 3.0 hours. Construct a 90% confidence interval for the hours of television watched per day in the population.

10. Alpha
Percent of confidence intervals that DO NOT contain the population mean over the long run
Probability this confidence interval DOES NOT contain the population mean
Width of confidence interval
Complement of confidence level

11. Efficiency
Extent to which the confidence interval clusters around the mean
Width of the confidence interval
Determined by population standard deviation and sample size

12. Confidence Intervals in SPSS
Give a 95% confidence interval for the number of children in an American family using GSS data.

13. In-Class
7.7 a & b