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STA 291 Fall 2009

STA 291 Fall 2009. Lecture 16 Dustin Lueker. Choice of Sample Size. Start with the confidence interval formula for a population proportion p ME denotes the margin of error Mathematically we need to solve the above equation for n. Choice of Sample Size.

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STA 291 Fall 2009

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  1. STA 291Fall 2009 Lecture 16 Dustin Lueker

  2. Choice of Sample Size • Start with the confidence interval formula for a population proportion p • ME denotes the margin of error • Mathematically we need to solve the above equation for n STA 291 Fall 2009 Lecture 16

  3. Choice of Sample Size • This formula requires guessing before taking the sample, or taking the safe but conservative approach of letting = .5 • Why is this the worst case scenario? (conservative approach) STA 291 Fall 2009 Lecture 16

  4. Facts about Confidence Intervals • The width of a confidence interval • Increases as the confidence level increases • Increases as the error probability decreases • Increases as the standard error increases • Increases as the sample size n decreases STA 291 Fall 2009 Lecture 16

  5. Confidence Interval for µ • α=.05, n=22 • tα/2= STA 291 Fall 2009 Lecture 16

  6. Example • A sample of 12 individuals yields a mean of 5.4 and a variance of 16. Estimate the population mean with 98% confidence. STA 291 Fall 2009 Lecture 16

  7. Sample Size • As with a confidence interval for the sample proportion, a desired sample size for a given margin of error (ME) and confidence level can be computed for a confidence interval about the sample mean • Why was t replaced by Z? • Found solving for ME in following confidence interval formula STA 291 Fall 2009 Lecture 16

  8. Example • Suppose we want a ME of 5 minutes and we think the standard deviation of download times is about 10 minutes. How large of a sample is needed if we are working with a confidence level of 95%? STA 291 Fall 2009 Lecture 16

  9. Confidence Interval for p • To calculate the confidence interval, we use the Central Limit Theorem (np and nq ≥ 5) • What if this isn’t satisfied? • Instead of the typical estimator, we will use • Then the formula for confidence interval becomes STA 291 Fall 2009 Lecture 16

  10. Example • Suppose a student in an advertising class is studying the impact of ads placed during the Super Bowl, and wants to know what the proportion of students on campus watched it. She takes a random sample of 25 students and finds that all 25 watched the Super Bowl. • Find a 95% confidence interval using first method learned for p • Find a 95% confidence interval using the new method if np, nq condition fails STA 291 Fall 2009 Lecture 16

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