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Confidence Intervals… continued

Confidence Intervals… continued. How confidence intervals behave. What we would like: High confidence Small margin of error Remember: For confidence intervals for population mean margin of error = . Margin of error = . How can we make it smaller? 1. Make z * smaller.

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Confidence Intervals… continued

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  1. Confidence Intervals…continued

  2. How confidence intervals behave • What we would like: • High confidence • Small margin of error Remember: For confidence intervals for population mean margin of error =

  3. Margin of error = • How can we make it smaller? 1. Make z* smaller. 2. gets smaller. 3. n gets larger.

  4. Example 10.6, p. 550 • Suppose that the manufacturer in Example 10.5 (p.546) wants 99% confidence rather than 90%. The critical value for 99% confidence is z* = 2.575. The 99% confidence interval for µ based on an SRS of 20 video monitors with mean mV is From Example 10.5, we had a margin of error of 15.8, giving the 90% confidence interval of

  5. Example 10.6, p. 550 • Suppose that the manufacturer in Example 10.5 (p.546) wants 99% confidence rather than 90%. The critical value for 99% confidence is z* = 2.575. The 99% confidence interval for µ based on an SRS of 20 video monitors with mean mV is 99 % confidence interval of 90% confidence interval of

  6. Margin of error • So how do we get a high confidence level with a small margin of error? PLAN AHEAD!!! We get to chooseour sample size!!!!

  7. Determining Sample Size • Example 10.7, p. 551 Company management wants a report of the mean screen tension for the day’s production accurate to within ±5 mV with 95% confidence. How large a sample of video monitors must be measured to comply with this request? So we want the margin of error (m) to be less than 5.

  8. For the a 95% confidence level, the critical value is . Example 10.5 told us that . So take a sample of at 285 video screens. • Example 10.7, p. 551

  9. Sample Size for Desired Margin of Error To determine the sample size nthat will yield a confidence interval for a population mean with a specified margin of error m, set the expression for the margin of error to be less than or equal to m and solve for n:

  10. Some Cautions with Confidence Intervals Any formula is correct only in specific circumstances: (some are listed on p. 553 in your book) • Data must be from an SRS from the population. • Formula not correct for more complex sampling designs • Fancy formulas can’t rescue badly produced data • Outliers can have a large effect on the confidence interval

  11. Some Cautions with Confidence Intervals Most importantly: The margin of error in a confidence interval covers only random sampling errors.

  12. Homework • P. 550: 10.8, 10.9 • P. 552: 10.12 • P. 554: 10.15, 10.17 DUE: Friday

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