1. Do Now For a sample of 20 songs, the average song length is 3.5 minutes with a standard deviation of 0.5 minute. Construct a 90% CI for the population mean. Assume the population is normal.

2. Confidence Intervals for Proportions We can also construct confidence intervals for proportions. For example, you can construct confidence intervals for elections, polls, surveys, etc.

3. Formula

4. Formula Explanation

5. Example In a survey of 100 students at Harlan, 60 students say their favorite sport to watch is basketball. Construct a 95% confidence interval for the proportion of students at Harlan who say their favorite sport to watch it basketball.

6. Solution First, you need “p hat” and “q hat”.

7. Critical z value Next, you need to find the critical z value. We use the normal distribution.

8. Put it all together

9. Solution continued…. 0.60 + 0.096 0.60 - 0.096 (0.696, 0.504) What can you infer about the population?

10. Inference You are 95% confident that the actual proportion of all students at Harlan who say their favorite sport to watch is basketball is between 69.6% and 50.4%.

11. Your calculator can do this! STAT TESTS 1-PropZInt x: 60 n: 100 C-Level: 0.95

12. Try it yourself! A sample of 510 adults in the U.S. found that 300 said “yes” when asked if they think global warming is real. Construct a 90% confidence interval for the actual proportion of all U.S. adults that would say “yes.”

13. And the answer is… (0.552, 0.624) You are 90% confident that the actual proportion of U.S adults that would say “yes” is between 55.2% and 62.4%

14. Another one! A sample of 715 teenagers found that 576 of them play video games for more than 6 hours per week. Construct a 99% confidence interval for the actual proportion of all teenagers that spend more than 6 hours per week playing video games.

15. And the answer is… (0.767, 0.843) You are 99% confident that the actual proportion of teenagers that spend more than 6 hours per week playing video games is between 76.7% and 84.3%.

16. And another one! In Chicago, you ask 810 residents if they use public transportation at least one per day. 519 said yes. Construct a 95% confidence interval for all residents in Chicago that would say they use public transportation at least once per day. (0.601, 0.673)