1. Statistics: Unlocking the Power of Data Lock 5 Section 6.2 Confidence Interval for a Single Proportion

2. Statistics: Unlocking the Power of Data Lock 5 Outline Confidence interval for a single proportion Determining sample size

3. Statistics: Unlocking the Power of Data Lock 5

4. Confidence Interval for p statistic  z*  SE

5. Statistics: Unlocking the Power of Data Lock 5 In March 2011, a random sample of 1000 US adults were asked “Do you favor or oppose ‘sin taxes’ on soda and junk food?” 320 adults responded in favor of sin taxes. Give a 95% CI for the proportion of all US adults that favor these sin taxes. Sin Taxes

6. Statistics: Unlocking the Power of Data Lock 5 Counts are greater than 10 in each category For a 95% confidence interval, z * = 1.96 Sin Taxes We are 95% confident that between 29.1% and 34.9% of US adults favor sin taxes on soda and junk food. (0.291, 0.349)

7. Statistics: Unlocking the Power of Data Lock 5 Sin Taxes

8. Statistics: Unlocking the Power of Data Lock 5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the sample proportion? A.280 B.500 C.56 D.0.56 E.1.96

9. Statistics: Unlocking the Power of Data Lock 5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the value of z*? A.0.56 B.1.28 C.1.645 D.1.96 E.2.576

10. Statistics: Unlocking the Power of Data Lock 5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the standard error? A.0.56 B.500 C.0.00049 D.0.0365 E.0.0222

11. Statistics: Unlocking the Power of Data Lock 5 In a random sample of 500 US citizens, 280 plan to vote in the upcoming election. We plan to construct a 90% confidence interval for the proportion of US citizens who plan to vote. What is the margin of error? A.0.56 B.500 C.0.00049 D.0.0365 E.0.0222 CI = statistic  margin of error

12. Statistics: Unlocking the Power of Data Lock 5 Margin of Error CI = statistic  margin of error

13. Statistics: Unlocking the Power of Data Lock 5 Margin of Error You can choose your sample size in advance, depending on your desired margin of error! Given this formula for margin of error, solve for n.

14. Statistics: Unlocking the Power of Data Lock 5 Margin of Error

15. Statistics: Unlocking the Power of Data Lock 5 Margin of Error Suppose we want to estimate a proportion with a margin of error of 0.03 with 95% confidence. How large a sample size do we need? (a)About 100 (b)About 500 (c)About 1000 (d) About 5000

16. Statistics: Unlocking the Power of Data Lock 5 Tongue Curling What proportion of people can roll their tongue?  Can you roll your tongue? (a) Yes(b) No  Visualize and summarize the data. What is your point estimate?  Give and interpret a confidence interval.  Tongue rolling has been said to be a dominant trait, in which case theoretically 75% of all people should be able to roll their tongues. Do our data provide evidence otherwise?