Math 151 , Spring 2005, Day 39 Wed. May 4 Hit reload After Class

Exam finished.  See Comments
Solutions are on reserve and outside my door.  Continue to work on the "right" answers to the test, please...
Day 38 Wed. May 4: (Re)Read  Chapter 23, Means; next Ch. 25, Paired Samples and Blocks. p. 483, Activstats uses the same dataset only does wife -husband, p. 25-1 activity 2.  Next, some of Ch 24, comparing (two) means.
Hand in 
Paired samples:
p. 449 #11 a,b,c Normal temperatures II
p. 491 #13 a-d (e optional) Sleep (by hand)  Use Table T to get a benchmark significance level, instead of P-value. (Optional, find the P-value using Activstats:  The table tool (23-1, activity 3) or T the Density tool  (Ch. 23--"normal dist" looking button on menu bar does t distribution))
E. Redo the Mileage example on the SPSS handout (back side).  The data is at   SPSS file, or in columns in Datasets page.
p. 489 # 7 Temperatures Use SPSS.  Data is on the lab computers, in  Math151 D&V\spss data files  D&V\dv01_25_07.sav
p. 493 # 22 Uninsured Use SPSS.  Data is on the lab computers, in  Math151 D&V\spss data files  D&V\uninsure.sav
p. 491 #12 Summer school Use SPSS. Type in the data.  Choose the columns so the Paired Data procedure subtracts the way you want it to.		 Read,
  to 
discuss 		 Optional 

Sample size: (by hand)
p. 449 #11 d Normal temperatures II
D.  What would be a good sample size if you want a 95% CI with  a ME no more than 1, and you think the standard deviation in the population is about 1?   Assume that sampling is very expensive, so you really want  the smallest n that will do the job. 

Homework questions? Day 38

Sample size for desired CI p. 441-2 will be OPTIONAL. (see Day 38 for discussion)
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Paired Samples (Chapter 25)   These same methods work on paired data--two measurements on same individual or on a matched pair of individuals.
   before--after, left hand--right hand, Drug A vs. Drug B on the same individual, or on a matched pair.
For each pair, find the difference in the observed values.  Then treat these differences as if they are "the" data set, from a normal population, and do One-sample t procedures.
Usually (always?) the null hypothesis will be " µ = 0", there is "no difference" between the treatments.
Example:  wax paper sandwich bags:  Is the wax layer the same inside and out?
25 bags:  measure (wax outside - wax inside) for each.  (pounds per square foot).
Differences:   xbar = .093,  s = .723   n = 25    SEM = .723/5 = .1446
H0 : µ = 0 (mean difference is 0)                  t = (.093 - 0)/SEM = .093/.1446 = .643.
Ha : µ Not = 0 (there is a difference)            t is less than .685 (d.f. = 24)
                                                                          which is right-tail t* for probability .25
       Because test is 2-sided, double the tail: .50.  P value is greater than .50.
                                           No evidence for difference.
Matched-pairs data (differences) are often more normal in shape than the separate variables ("oddness" is often the same for both items in a pair, and disappears in subtraction.  Another reason why this is a nice experimental design. )

SPSS for Matched pairs:  See Handout, backside of One-Sample t.  (ActivStats p. 25-1, Activity 2)
--You can use the built-in Analyze>Compare Means>Paired-Samples T-Test.
   Disadvantages:  It always subtracts the rightmost variable from the leftmost.  You don't get a list of the differences.
--Create a new variable of the Differences:  Transform>Compute:
       Target variable: Difference, Numeric Expression: firstVariable - secondVariable.
       Do One Sample on Difference.
Handout example:  SPSS file,  in columns in Datasets page.

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