2. CONFIDENCE INTERVALS n point estimate: estimate exact value – precise – likely to be wrong n interval estimate: range of values – less precise – less likely to be wrong

3. What a Confidence Interval Tells You 1. Range of values 1. Range of values 2. Level of confidence 2. Level of confidence n No hypothesis is directly tested

4. Confidence Interval with z- scores n Purpose: provide a range of values containing the population mean n Design: any design where a mean is calculated n Assumptions: same as for z-test

5. How it Works n Start with your sample mean as the middle of the interval. n Establish upper and lower limits depending on how confident you want to be.

6. upper limit lower limit 

7. Computation of Confidence Interval with z-scores

8. Example A sample of 25 students took an aptitude test with a population standard deviation of 40. The mean of the 25 students was 500. Compute the 95% confidence interval for the mean. A sample of 25 students took an aptitude test with a population standard deviation of 40. The mean of the 25 students was 500. Compute the 95% confidence interval for the mean.

9. STEP 1: Compute the standard error. STEP 1: Compute the standard error.

10. STEP 2: Find the z score for your confidence level. For 95% confidence, use z = 1.96 For 99% confidence, use z = 2.58 z = 1.96

11. STEP 3: Compute the lower and upper limits. STEP 3: Compute the lower and upper limits.

12. APA Format Sentence The 95% confidence interval for the mean aptitude test score was 484.32 - 515.68.

13. Confidence Interval with t- scores n Purpose: provide a range of values containing the population mean n Design: any design where a mean is calculated n Assumptions: same as for single sample t- test

14. Computation of Confidence Interval with t-scores

15. Example 64 research participants were timed on a motor task. Their mean time was 20 sec, with s = 4.00. Compute the 99% confidence interval for the mean. 64 research participants were timed on a motor task. Their mean time was 20 sec, with s = 4.00. Compute the 99% confidence interval for the mean.

16. STEP 1: Compute the standard error. STEP 1: Compute the standard error.

17. STEP 2: Find the t score for your confidence level. Look up two-tailed t in table, using df = N-1, and 1- level of confidence for  df = 64-1=63  = 1-.99=.01 two-tailed t = 2.660

18. STEP 3: Compute the lower and upper limits. STEP 3: Compute the lower and upper limits.

19. APA Format Sentence The 99% confidence interval for the mean time to complete the task was 20 sec +/- 1.33.

20. Confidence Interval for a Proportion n Purpose: provide a range of values containing the population proportion n Design: any design where a proportion or percent is calculated n Assumptions: –representative sample –independent observations

21. Computation of Confidence Interval for a Proportion

22. Example A sample of 500 registered voters rated how well the President is doing his job. The proportion who gave him a “good” rating was.52, or 52%. Compute the 95% confidence interval for the proportion. A sample of 500 registered voters rated how well the President is doing his job. The proportion who gave him a “good” rating was.52, or 52%. Compute the 95% confidence interval for the proportion.

23. STEP 1: Compute the standard error. STEP 1: Compute the standard error.

24. STEP 2: Find the z score for your confidence level. For 95% confidence, use z = 1.96 For 99% confidence, use z = 2.58 z = 1.96

25. STEP 3: Compute the lower and upper limits. STEP 3: Compute the lower and upper limits.

26. APA Format Sentence The 95% confidence interval for the proportion of “good” ratings was.52 +/-.04.

27. Changing the Width of a Confidence Interval n A wider interval is less precise and therefore less informative. n The interval will be narrower with – a larger sample – lower variability – a lower level of confidence

28. Margin of Error n The media often report poll results and include margin of error. This is the +/- part, usually in fine print. n Add and subtract the margin of error to get the confidence interval

29. Margin of Error n Can be used as an indirect test of significance n Construct confidence interval around sample statistic using margin of error n If interval includes Ho value, difference is not significant