1 / 12

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.

ardice
Télécharger la présentation

Confidence Intervals… continued

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related