Math 151 , Day 35, Wednesday, April 25, 2007  After class. hit reload...

HW Day35 . Read ahead Please!  P. 355, choosing n for a desired C and m.   Check,  sample size 14.17.  Chapter 15, Signifincance testing (the "other" big topic in inference)
Moore Ch. 14, Day 35  Hand in Monday 

A.  New Shoeboxes: On a Separate sheet:  (2 shoeboxes. )The shoeboxes are outside my door if you missed doing them in class. For each sample of size  4 from a shoebox, write down the values, find the mean, (know which box you got them from: White #s, green box. Yellow, red top.) and tell whether you believe the population mean for that box is 20, or something bigger. (Your gut feeling.) Does it help to know that the standard deviations for the shoeboxes are both 4? ( Bring your sample numbers and xbars  to class  to pool.)   (This is related to Chapter 15, where we'll learn the formal methods.)

Read, 
to discuss 		Optional
A few  problems good to review for the exam
p. 419, 17.7 Day care, parameter or statistic
p. 422, 17.27 and 28 means vs. individuals.  In #27, they're taking the "about what range" to be the interval containing the middle 99.7%--almost all. (Answer to last question of #28 is
"no"--histogram of individual values in sample will be distributed (roughly) like the population.)
p. 421, 17.26 WAIS, n = 1, n = 60 (Answers: a) about .3707, b) 100, 1.936, c).0049, d) a could be quite different; b still correct, c approx. right bcs of Central Lim. Th.))
Exam 4 this Friday (next class).  Covers  Ch. 10 p. 250 on (Discrete and Continuous models and R.V.'s), Ch. 11 up to p. 286 only, Ch. 14 to p.354, Ch. 16 to p. 391. (i.e. thru Day 34 HW).   Sample Exam is good as written. (Handed out Fri. Outside my door..)  Solutions .
   Sign up Today. for 10:30 start:  Confirm with me any other time to take it.

     Buffer against one low hour exam:
The final % exam grade minus 10 points will be substituted for the lowest hour exam grade, if it is higher.

Examples:
Ex1 Ex2 Ex3
 Ex4 final % final -10
Student 1 Original 85 80 85
 60 85 75, replaces lower 60
Treated 85 80 85
 75 85 <--ß These will be used.
Student 2 Original 85 80 80
 70 75 65, lower than 70, don't replace.
Treated 85 80 80
 70 75
Student 3 Original 85 50 75
 55 85 75, replaces lower 50
Treated 85 75 75
 55 85 <--ßThese will be used
This is to encourage those who are nervous about Exam 4, and to encourage all to try to put it together for the final.
New Shoeboxes: On a Separate sheet:  (2 shoeboxes. )The shoeboxes are outside my door if you missed doing them in class.  From each shoebox, take a sample of size 4, and write down the values.  (know which box you got them from: White #s, green box. Yellow, red top.)   Do A above for HW.

  Note:  11.38 and 11.39 are "backward" Normal distribution problems:  going from proportion/probability to x (here L).  I didn't discuss these in class.  We'll postpone discussing these till Chapter 15 (Today if no other questions, Probably Monday.)
I forgot to say this last time: How big does n have to be before the sampling distribution of the x-bars is "normal enough"? (Central Limit Theorem) The more symmetrical and unimodal the population, the smaller n needs to be.  However, unless a distribution is quite skewed or bumpy, by n = 25 it's roughly normal.  See Day 29, bottom, play with applet.

"Fuzzy Central Limit Theorem:"
Data whose variation is due to  many   small    independent   random influences will have an approximately normal distribution.
  Balls and pins, heights of women, etc.  (p. 281, after the yellow box)

Confidence intervals, Day 34
Homework questions?    Day 34
Homework 14.34 and 14.35 , p. 160.     
     14.35:    T = true value of parameter,  * = value of this statistic  * = results of other surveys
                           ** *
                        * ******
               * * ** ******T**** *** ** * *   
Clustering will be around True value, not around the one we got this time.
General exam questions?

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