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CONFIDENCE INTERVALS

CONFIDENCE INTERVALS. point estimate : estimate exact value precise likely to be wrong interval estimate : range of values less precise less likely to be wrong. What a Confidence Interval Tells You. 1. Range of values 2. Level of confidence No hypothesis is directly tested.

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CONFIDENCE INTERVALS

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  1. CONFIDENCE INTERVALS • point estimate: estimate exact value • precise • likely to be wrong • interval estimate: range of values • less precise • less likely to be wrong

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

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

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

  5. lower limit upper limit M

  6. Computation of Confidence Interval with z-scores

  7. 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.

  8. STEP 1: Compute the standard error.

  9. 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

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

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

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

  13. Computation of Confidence Interval with t-scores

  14. 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.

  15. STEP 1: Compute the standard error.

  16. 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 a. • df = 64-1=63 • a = 1-.99=.01 • two-tailed t = 2.660

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

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

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

  20. Computation of Confidence Interval for a Proportion

  21. 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.

  22. STEP 1: Compute the standard error.

  23. 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

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

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

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

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

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

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