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6.5 B: Extension-Estimating a Population Proportion

Objective : To estimate population proportions with various confidence levels when specific conditions are not met. 6.5 B: Extension-Estimating a Population Proportion. When the Success/Failure Condition fails, all is not lost.

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6.5 B: Extension-Estimating a Population Proportion

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  1. Objective: To estimate population proportions with various confidence levels when specific conditions are not met 6.5 B: Extension-Estimating a Population Proportion

  2. When the Success/Failure Condition fails, all is not lost. • A simple adjustment to the calculation lets us make a confidence interval anyway. • All we do is add four fakeobservations, two successes and two failures. • So instead of we use the adjusted proportion A Confidence Interval for Small Samples

  3. Now the adjusted interval is • The adjusted form gives better performance overall and works much better for proportions of 0 or 1. • It has the additional advantage that we no longer need to check the Success/Failure Condition. A Confidence Interval for Small Samples (cont.)

  4. Surgeons examined their results to compare two methods for a surgical procedure used to alleviate pain ion the outside of the wrist. A new method was compared with the traditional “freehand” method for the procedure. Of 45 operations using the “freehand” method, three were unsuccessful, for a failure rate of 6.7%. With only three failures, the data don’t satisfy the Success/Failure Condition, so we can’t use a standard confidence interval. What is a 95% confidence interval using the “plus-four” method? Example

  5. AP Book Work • Please find the pages and book numbers using the CHS Statistics online calendar. Assignment

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