1 / 7

Friday Oct 8

Friday Oct 8. Confidence interval for  How to obtain Z /2 Interpretation of confidence interval What n  30, can replace  by s Read 5.2 Next time: read 5.3. Similarly P(-1.96 < Z < 1.96) = 0.95 Thus P( Ў -1.96  Ў <  < Ў +1.96  Ў ) = 0.95

nau
Download Presentation

Friday Oct 8

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. Friday Oct 8 • Confidence interval for  • How to obtain Z/2 • Interpretation of confidence interval • What n  30, can replace  by s • Read 5.2 • Next time: read 5.3

  2. Similarly P(-1.96 < Z < 1.96) = 0.95 • Thus P(Ў-1.96Ў <  < Ў+1.96Ў) = 0.95 • For a 99% confidence interval: • P(-2.58 < Z < 2.58) =0.99. Z0.005=2.58 • Thus P(Ў -2.58Ў <  < Ў+2.58Ў) = 0.99

  3. Formula for 100(1-)% confidence interval for  • when  is given is • [Ў Z/2* Ў] where Ў = /n • Z/2 is a value of Z having a tail area of /2 to its right Histogram of C1, with Normal Curve f(y) 3 a/2 a/2 2 m +Za/2 s y m-Za/2 s 1 0

  4. A few frequently used Z value • 90% C. I.  = .1 Z/2 = Z.05 = 1.645 • 95% C. I.  =.05 Z/2 = Z.025 = 1.96 • 99% C. I.  =.01 Z/2 = Z.005 = 2.575 • 97% C. I.  =.03 Z/2 = Z.015 = 2.17

  5. Example • E.g. 5.10 Recent data from a national survey of 1350 women indicated that the average woman goes to a hair salon once every 5 weeks and spends on the average $26.49. With a standard deviation (s) of $12.00. Use these data to construct a 99% C.I. for  (average amount spent by women in America on hair salon). • n = 1350, Ў = 26.40,  = s = 12,  = 0.01 99% C.I. : Ў  Z0.005.121350 = 26.40  2.58 . 0.3266 (25.56, 27.24) 99% C.I. for  • Verbal interpretation of the 99% C.I. : We are 99% confident that the average amount a woman in America spends in a hair salon is between $25.56 and $27.24.

  6. e.g. 5.15 900 high-school graduates sampled. Objected of interest: distance between the high school attended and present address. Ў = 430 miles, s = 262 miles. Find • a. 95% CI for “average distance between a person’s present address and high school”  = 1 - 0.95 = 0.05 Ў ± Z/2*n, Ў =430, Z/2 = Z0.025 =1.96. n = 900 430 ± 1.96*262900 (412.88, 447.12) width = 34.24 • b. 99% Confidence interval 430 ± 2.58* 262900 (407.468; 452.532) width = 45.064

More Related