Chapter 7 Confidence Intervals and Sample Size for Proportions

1. Chapter 7 Confidence Intervals and Sample Size for Proportions

2. Does Success Bring Happiness? W.C. Fields said “Start everyday off with a smile and get it over with.” Do you think people are happy because they are successful or successful because they are happy? Vote now. pollEV.com

3. 7.3 Confidence Intervals and Sample Size for Proportions p = population proportion (read p “hat”) = sample proportion For a sample proportion, where X = number of sample units that possess the characteristics of interest and n = sample size. Bluman Chapter 7

4. Example 7-8: Air Conditioned Households In a recent survey of 150 households, 54 had central air conditioning. Find and , where is the proportion of households that have central air conditioning. Since X= 54 and n= 150, Bluman Chapter 7

5. Example: Happiness Find , where is the proportion of people who believe they are successful because they are happy. Bluman, Chapter 7

6. Formula for a Specific Confidence Interval for a Proportion when np 5 and nq 5. Rounding Rule: Round off to three decimal places. Bluman Chapter 7

7. Example 7-9: Covering College Costs A survey conducted by Sallie Mae and Gallup of 1404 respondents found that 323 students paid for their education by student loans. Find the 90% confidence of the true proportion of students who paid for their education by student loans. Bluman Chapter 7

8. Example 7-9: Covering College Costs Since α = 1 – 0.90 = 0.10, zα/2 = 1.65. Bluman Chapter 7

9. Example 7-9: Covering College Costs You can be 90% confident that the percentage of students who pay for their college education by student loans is between 21.1 and 24.9%. Bluman Chapter 7

10. Example 7-10: Religious Books A survey of 1721 people found that 15.9% of individuals purchase religious books at a Christian bookstore. Find the 95% confidence interval of the true proportion of people who purchase their religious books at a Christian bookstore. You can say with 95% confidence that the true percentage is between 14.2% and 17.6%. Bluman Chapter 7

11. Example: Happiness Find the 90% confidence of the true proportion of people who believe that that people are successful because they are happy. Bluman, Chapter 7

12. Formula for Minimum Sample Size Needed for Interval Estimate of a Population Proportion If necessary, round up to the next whole number. Bluman Chapter 7

13. Example 7-11: Home Computers A researcher wishes to estimate, with 95% confidence, the proportion of people who own a home computer. A previous study shows 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. The researcher should interview a sample of at least 2305 people. Bluman Chapter 7

14. Chapter 7Confidence Intervals and Sample Size Section 7-3 Example 7-12 Page #380 Bluman Chapter 7

15. Example 7-12: M&M Colors A researcher wishes to estimate the percentage of M&M’s that are brown. He wants to be 95% confident and be accurate within 3% of the true proportion. How large a sample size would be necessary? Since no prior knowledge of is known, assign a value of 0.5 and then = 1 – 0.5 = 0.5. Substitute in the formula, using E = 0.03. Bluman Chapter 7

16. Example 7-12: M&M Colors Bluman Chapter 7

17. Example: Happiness If we wished to be accurate within 2.5% on our happiness question, how large of a sample would we need to take? Bluman, Chapter 7

18. Internet Access Do you frequent your Facebook page at least once a day? Do you have a landline phoneline at home? Vote Now: Pollev.com Bluman, Chapter 7

19. Internet Access Construct a 95% confidence interval for the true proportion who frequent it at least once a day. How large of a sample would be need to be accurate within 2%? Bluman, Chapter 7