MATH 251, Probability and Statistics I, Fall 2001, Mon. Dec. 3, Day 38

HW Day 38 (Re)read 7.2, including the * parts.
Read ahead:  7.3, we will cover pp.566-7, inference for population spread, and p. 570, robustness.

Sec. 7.2   Hand in:  Pooled-sample (equal sigma's).  Pooled-sample computation gets a bigger d.f. and therefore a shorter CI & smaller p-value than the unequal variances method, on the same data.  7.65 and 7.77 rowing--weight.  (unequal and equal methods compared.) 7.75 social insight. By hand.  this is Example 7.16, p. 546, not 526. - - - - - - - - - - - - - - - - - - - - - - - - - - - -  Some algebra:  General advice on designing experiments is to put equal numbers into each sample if you can.  Here's some hints why.  A)  If n1= n2 then the expression for the standard error of (xbar1 -xbar2 ), i.e. the denominator of the t-statistic, is the same for the unequal variances version p. 541  and for the pooled-t p.551.  Use algebra to show they are the same (set n= n1= n2).  [Thus the only difference in computing with the different versions in this case will be the d.f. you use]  B) If n1= n2 = n and  s1= s2 =s, the complicated df formula on p. 549 collapses into  df = 2n - 2 (= n1 + n2 - 2).  Use algebra to show it. [So at least for equal n's and similar s's, the complicated  df formula will not lose you much sharpness compared to the pooled  version.  ] = = = = = = = = = = = = = = = = = = = = Hand in:  These problems review chapter 7 (and a bit of 6), give more "realistic" settings and problems. All can be done without SPSS.  The only use of SPSS might be to get p-values  from t's, but you can use the approximate table results if it's easier..     p.582, 7.119  sample size and n     p. 576, 7.98 weight-loss--interpret     p.577, 7.100  pins in holes     p.578, 7.102, 103, 104 London bus guys     p.579, 7.106 mean pop, Cal. co.     p.580, 7.108 a and b only. city/country pollution.

Read, discuss

Optional (more practice)