1. Statistics: Concepts and Controversies What Is a Confidence Interval?
Chapter 21
What Is a Confidence Interval?
Chapter 15
Chapter 15

2. Recall from previous chapters:
Parameter
fixed, unknown number that describes the population
Statistic
known value calculated from a sample
a statistic is used to estimate a parameter
Sampling Variability
different samples from the same population may yield different values of the sample statistic
estimates from samples will be closer to the true values in the population if the samples are larger.
Chapter 21

3. The Rule for Sample Proportions
Chapter 21

4. Rule Conditions and Illustration
Statistical Thinking
Rule Conditions and Illustration
For rule to be valid, must have
1. Random sample
2. ‘Large’ sample size
Chapter 21
Chapter 21

5. Case Study: Fingerprints A Question
Assume that the proportion of all men who have leftward asymmetry is 15%.
Is it unusual to observe a sample of 66 men with a sample proportion ( ) of 30% if the true population proportion (p) is 15%?
Chapter 21

6. Case Study: Fingerprints Answer to Question
Where should about 95% of the sample proportions lie?
mean plus or minus two standard deviations
0.15  2(0.044) = 0.062
(0.044) = 0.238
95% should fall between & 0.238
Chapter 21

7. Formula for a 95% Confidence Interval
sample proportion plus or minus two standard deviations of the sample proportion:
Chapter 21

8. Formula for a 95% Confidence Interval
standard error (estimated standard deviation of )
Chapter 21

9. Margin of Error
(plus or minus part of C.I.)
Chapter 21

10. Formula for a C-level (%) Confidence Interval for the Population Proportion
where z* is the critical value of the standard normal distribution for confidence level C
Chapter 21

11. Common Values of z*
Chapter 21

12. Gambling on Sports A December 2007 Gallup Poll con-sisting
of a random sample of 1027 adult Americans
found that 17% had gambled on sports in the
last 12 months. Find a 95% confidence interval
for the proportion of all adult Americans who
gambled on sports in this time period. How
would you interpret this interval?
Chapter 21

13. A 99% confidence interval
The BRFSS random sample of 2166 college
graduates in California in 2006 found that
279 had engaged in binge drinking in the past
year. We want a 99% confidence interval for
the proportion p of all college graduates in
California who engaged in binge drinking in the past year.
Chapter 15

14. Our statistical software has a “random number generator” that is supposed to produce numbers scattered at random between 0 to 1. If this is true, the numbers generated come from a population with μ = 0.5. A command to generate 100 random numbers gives outcomes with mean x = and s = Give a 90% confidence interval for the mean of all numbers produced by the software.
Chapter 15

15. We would like to estimate the mean GPA of the population of all WSU undergraduates. We would like to compute a 90 percent confidence interval for this mean, and we would like our interval to have margin of error no greater than 0.1. The Registrar's Office says that a reliable guess of the population standard deviation is 0.5. What is the smallest number of students we should recruit to achieve our goals?
Chapter 15