1 / 16

Parameter Estimation

Parameter Estimation. Chapter 8 Homework: 1-7, 9, 10. Parameter Estimation. Know X ---> what is m ? Point estimate single value: X and s compute from sample Confidence interval range of values probably contains m ~. Parameter Estimation. How close is X to m ?

tbenitez
Télécharger la présentation

Parameter Estimation

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. Parameter Estimation Chapter 8 Homework: 1-7, 9, 10

  2. Parameter Estimation • Know X ---> what is m ? • Point estimate • single value: X and s • compute from sample • Confidence interval • range of values • probably contains m ~

  3. Parameter Estimation • How close is X to m? • look at sampling distribution of means • Probably within 2 s X • Use: P=.95 • or .99, or .999, etc. ~

  4. Critical Value of a Statistic • Value of statistic • that marks boundary of specified area • in tail of distribution • zCV.05= ±1.96 • area = .025 in each tail ~

  5. .025 .025 -2 -1 0 1 2 +1.96 -1.96 Critical Value of a Statistic f .95 z

  6. Confidence Intervals • Range of values that m is expected to lie within • 95% confidence interval • P=.95 mwill fall within range • level of confidence • Which level of confidence to use? • Cost vs. benefits judgement ~

  7. < m< (s X) (s X) (s X) X - zCV X + zCV X ±zCV Lower limit Upper limit or Finding Confidence Intervals • Method depends on whether s is known • If s known

  8. When s Is Unknown • Usually do not know s • s is “best”point-estimator • standard error of mean for sample

  9. When s Is Unknown • Cannot use z distribution • 2 uncertain values: mands • need wider interval to be confident • Student’s t distribution • normal distribution • width depends on how well s approximates s ~

  10. Student’s t Distribution • if s = s, then t and z identical • if s¹ s, then t wider • Accuracy of s as point-estimate • larger n ---> more accurate • n > 120 • s»s • t and z distributions almost identical ~

  11. Degrees of Freedom • Width of t depends on n • Degrees of Freedom • related to sample size • larger sample ---> better estimate • n - 1 to compute s ~

  12. Critical Values of t • Table A.2: “Critical Values of t” • df = n - 1 • level of significance for two-tailed test • a • total area in both tails for critical value • level of confidence for CI ~ • 1 - a ~

  13. Critical Values of t • Critical value depends on degrees of freedom & level of significance df .05 .01 1 12.706 63.657 2 4.303 9.925 5 2.571 4.032 10 2.228 3.169 30 2.042 2.750 60 2.000 2.660 120 1.980 2.617 ¥ 1.96 2.576

  14. (sX) X ±tCV < m < (sX) (sX) X - tCV X + tCV Lower limit Upper limit or [df = n -1] Confidence Intervals: s unknown • Same as known but use t • Use sample standard error of mean • df = n-1 [df = n -1]

  15. Examples: Confidence intervals • What is population mean for high school GPA of Coe students? • If s unknown? • X = 3.3 s = .2 n = 9 • What if n = 4? • 99% CI ?~

  16. Factors that affect CI width • Would like to be narrow as possible 1. Increasing n • decreases standard error • increases df 2. Decreasing s or s • little control over this 3. s known 4. Decreasing level of confidence • increases uncertainty ~

More Related