MATH 251, Probability and Statistics I, Fall 2001, Wed. Nov. 14, Day 32

Quiz Friday:  to write down these definitions (memorize them):  I want the general definitions, not just formulas for the tests of µ.
Level C confidence interval for a parameter.
P-value for a test.
"A test is significant at level alpha = .05 if the P-value__________________"

ReRead Tests of Significance (sec. 6.2).  Read  pp. 463-466 "two-sided tests and confidence intervals"
Read 6.3  It is important stuff, but they say it as well as or better than I can.  So  I will lecture only briefly on it;  I will go over the reasoning of the "77 tests" (pp.479-80).  Additions to the summary, p. 481:
Spirit of the approach:
    P-value--"assessment of the evidence against H0"--communication of results, decisions left to reader. (Science at its best)  vs. Testing at fixed significance level alpha--"decide against H0 if P-value < alpha."  (business)
You cannot legitimately test a hypothesis on the same data that first suggested that hypothesis. (p.480) Every data set will turn up with some unusual pattern if you examine it hard enough.  (If you must explore and confirm with the same data set, one way is to (randomly) take half the data set, explore and generate hypotheses; then use the other half for confirmatory tests.)

Handout on Hawthorne Effect (given out in class today)--The Hawthorne Effect and the Placebo Effect are different but seem to share a common ground in our natures as social beings--people respond positively to being paid attention to, in very deep ways.

ReRead Cautions, p. 444-5--they apply to tests too.
.
We will either postpone or omit  6.4; I am anxious to get through chapter 7.
Hand in:   Sec. 6.2  I have arranged these in what seems to me to be the logical pedagogical order, so please try them in this order.
Significance and table D--one sided/two sided
6.45, 6.44 one sided, two sided State your answers as 
         "P is between ___ and ___",  or  "___ < P < ____"
6.46  one sided/two sided.  You can use table D for this, but be careful with the 2 sided.
6.42, 6.47 (Note it's two-sided) You may find it easier, as far as reasoning through what is happening, to do 6.47 first.  The idea in 6.42 is that it is enough to compare your z with the z* values for .05 and .01; save yourself any more computation (like 6.46).  But usually we would like the most precise measure of p-value we can get--if we don't have a z-table, it will just be the approximation from table D, like problems 6.45, 44. 
6.43 1%, 5%


Review
p. 475 6.51 patents
p. 499  6.84, 85 "significance"

CI level C <-->2-sided test with sig. 1-C.
p. 474, 6.49 runners
I was going to assign 6.48 but I don't think it is a very good practical example.  The alternative hypothesis here amounts to "detectors are inaccurate on average" which is kind of a strange thing to want to prove.  Since most consumers will have only one, not 12 to take an average with, I would be more interested in something like the chances that an individual one that I buy will be off ( that might require estimating the standard deviation of the population of detectors.)


Sec. 6.3 
6.53 rhetorical questions, i hope
6.54 strong evidence for C?
6.56, 56  big sample size can prove (almost) anything... 
6.57 knife-edge decision making?
6.59 500 tests.
A. You have a theory that walls painted pale pink will have a mellowing effect on elementary school students and produce better grades.  So you receive permission to repaint one classroom  from each grade at the local school over Christmas vacation (the others stay as they were).  Indeed, the students in the pink classrooms do better on end-of-year tests.  What criticism can be made of your experiment, and how could it have been designed to avoid this?
Read, discuss
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


Sec. 6.3
6.58 This should be old stuff now...
 
Optional
(more practice)
6. 41


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