1 / 9

Confidence Intervals

Confidence Intervals. Mon, March 22 nd. Point & Interval Estimates. Point estimate – use sample to estimate exact statistic to represent pop parameter Point estimate of average Amer salary = $29, 340

dacian
Download Presentation

Confidence Intervals

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 Mon, March 22nd

  2. Point & Interval Estimates • Point estimate – use sample to estimate exact statistic to represent pop parameter • Point estimate of average Amer salary = $29, 340 • Interval estimate – use sample to estimate a range of values within which pop parameter may fall (Confidence Interval) • Interval estimate of average salary = $27,869 to $30,811

  3. (cont.) • With confidence interval, specify likelihood this interval will contain the pop parameter • 95% conf interval, means we are 95% confident the interval/range contains the true pop parameter • Almost always choose 90, 95, or 99% confidence

  4. Constructing Confidence Interval • 1) Calculate standard error of the mean ybar = y / sqrt N • 2) Decide on confidence level (90/95/99) – then find corresponding z value • We know that, for a normal curve, 68% of the scores will fall betw + or – 1SD (std error), so • 95% will fall betw + or – 1.96 SE (see normal curve table for .05 / 2 tails, so z = + or –1.96 • 99% will fall betw + or –2.58 SE (see normal curve table for .01 / 2 tails, so z = + or – 2.58)

  5. (cont.) • 3) Use Conf Interval formula: CI = Ybar + and – Z(ybar ) • 4) Interpret results Ex) Find 95% CI for average commuting time when ybar = 7.5 hrs, y = 1.5 and sample N=500 *Find standard error, ybar = 1.5 / sqrt(500) = .07

  6. example • For 95% CI, z value is 1.96 (see table 12.1 for z values for 90/95/99% CI) • 95% CI = 7.5 + and – 1.96(.07) = 7.36 to 7.64 • (7.36, 7.64) • Interpretation – we are 95% confident the true commuting time of the pop is between 7.36 and 7.64 hrs per week)

  7. Example (cont.) • Notice what happens to CI when we increase confidence to 99% • Corresponding z for 99% = 2.58, so • 99% CI = 7.5 + and – 2.58(.07) = 7.32 to 7.68 • Now only 1% risk we are wrong, but a wider, less precise, interval

  8. Estimating ybar • If not given y and only given Sy (sample std dev), can estimate Sybar (rather than ybar) • Sybar = Sy / sqrt N

  9. Sample Size and CI • Increase N and increase precision of CI (range becomes smaller): • Due to smaller standard error • Earlier example, increase N from 500 to 2500, ybar = 1.5 / sqrt(500) = .07 ybar = 1.5 / sqrt(2500) = .03 CI = 7.5 + and – 1.96(.03) = 7.44 to 7.51 Compared w/7.36 to 7.64 (w/ .07 std error)

More Related