Confidence Intervals - Proportions

1. Confidence Intervals - Proportions

2. Objective Construct a Proportion Confidence Interval and Find Sample Size.

3. Relevance Can Estimate Population Parameters from Sample Statistics

4. Remember……

5. If x = the number of successes and n = the number of trials then

6. Finding the sample proportion if not given…… • In a survey of 250 households, 178 had radios.

7. Proportion Confidence Interval……

8. Example…… • A sample of 200,000 was taken on most popular boat names. 6% are named “Osprey.” Find a 95% confidence interval of the true proportion of boats named “Osprey.”

9. Answer……

10. Example…… • In a sample of 1001 U.S. adults, 58% think that airplanes are the safest mode of transportation. Construct a 99% confidence interval.

11. Answer……

12. Example…… • A sample of 500 nurses included 60 men. Find the 90% confidence interval of the true proportion of men who applied to the nursing program.

13. Answer……

14. Confidence Intervals - Proportions Finding Sample Size

15. Finding Sample Size of a Proportion…… • Formula:

16. Example…… • Estimate with 95% confidence the number of people who own a home computer. A previous study showed that 40% of those interviewed had a computer at home. The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size necessary.

17. Values: Plug In: Answer……

18. You Try…… • A researcher wishes to estimate the proportion of executives who own a car phone. A previous study showed that 50% owned a car phone. She wants to be 90%confident and be accurate to within 5% of the true proportion. Find the minimum sample size necessary.

19. Values: Plug In: Answer……