1. C ONFIDENCE INTERVALS FOR PROPORTIONS Sec 9.3

2. T HE P LAN ; F OR BUILDING A 95% CONFIDENCE INTERVAL

3. What do we use for (se)

4. W HAT TO USE FOR S TANDARD E RROR, The standard error for a sampling distribution of proportions is normally; Sense we don’t know p we will use instead, where is our sample proportion. This will give us a strong approximation for the true standard error.

5. T HE P LAN ; F OR BUILDING A 95% CONFIDENCE INTERVAL

6. In general: For proportional data Our confidence interval is found by finding; Sample proportion Z-score for confidence level Standard Error or

7. R EMINDER ABOUT SAMPLE SIZE ; Since we are working with proportional distributions we need to be sure that our sample size is large enough for the central limit theorem to give us a normal distribution to work with. The sample size must be large enough so that; and

8. L ETS TRY ;.735 73.5% of Americans have cranberries at thanksgiving. You are tasked with finding out the proportion of American households that will have cranberries with their Thanksgiving meal. Step one: Find a point estimate Step two: Build a 95% confidence interval

9. L ETS TRY ; 73.5% Step One: Using a sample you randomly survey 100 American and find that 70 of plan on having cranberries. This gives you a point estimate of.7000

10. L ETS TRY ; 73.5% Step Two: We need to find the standard error in order to build our intervals.

11. L ETS TRY ; 73.5% Step Two: We need to find the standard error in order to build our intervals.

12. L ETS TRY ; 73.5% Step Two: We need to find the standard error in order to build our intervals. So our interval is; The interval from 61.02% to 78.98% Margin of error

13. L ETS TRY ; 73.5% Therefore we are 95% confident that between 61% and 79% of Americans will be having cranberries with their Thanksgiving meal.

14. Y OU T RY ; A sample of 1500 dogs finds that only 1037 of them are “altered”. Find a 95% confidence interval for the population proportion of altered dogs.

15. O THER CONFIDENCE L EVELS : We can find confidence intervals with other confidence levels. The most common are 90%, 95%, and 99%. The only difference is the z-score we will use needs to be changed to model the new confidence level. Here are the z-scores for these common confidence levels

16. Y OU T RY ; A sample of 1500 dogs finds that only 1037 of them are “altered”. Find a 99% confidence interval for the population proportion of altered dogs.

17. P OSSIBILITIES ; Is it possible that our confidence interval does not contain the population proportion? Oh yes, and this will happen 5% of the time with a 95% confidence interval.