title: Testing For Normality (STATISTICS, A SERIES OF TEXTBOOKS AND MONOGRAPHS)
author:  Henry C. Thode 
description: this clearly written comprehensive and thoroughly researched work provides much useful information and should probably be on the shelves of every research-oriented department's library.<br /><br />- Mathematical Reviews, Issue 2004d
zlib_text:  
  261 
  CHAPTER 9 
   
  Section 9.1 
   
  1. 
   
  a. 
  (
  )
  ( )
  ( )
  4.
  5.4
  1.4
  −
  =
  −
  =
  −
  =
  −
  Y
  E
  X
  E
  Y
  X
  E
  , irrespective of sample sizes. 
   
  b. 
  (
  )
  ( )
  ( )
  (
  )
  (
  )
  0724
  .
  100
  0.2
  100
  8.
  1
  2
  2
  2
  2
  2
  1
  =
  +
  =
  +
  =
  +
  =
  −
  n
  m
  Y
  V
  X
  V
  Y
  X
  V
  σ
  σ
  , and the s.d. 
  of  
  2691
  .
  0724
  .
  =
  =
  −Y
  X
  . 
   
  c. 
  A normal curve with mean and s.d. as given in a and b  (because m = n = 100, the CLT 
  implies that both X  and Y  have approximately normal distributions, so 
  Y
  X −
   does 
  also).  The shape is not necessarily that of a normal curve when m = n = 10, because the 
  CLT cannot be invoked.  So if the two lifetime population distributions are not normal, 
  the distribution of 
  Y
  X −
   will typically be quite complicated. 
   
   
  2. 
  The test statistic value is 
  n
  s
  m
  s
  y
  x
  z
  2
  2
  2
  1 +
  −
  =
  , and Ho will be rejected if either 
  96
  .1
  ≥
  z
   or 
  96
  .1
  −
  ≤
  z
  .  We compute 
  85
  .4
  33
  .
  433
  2100
  45
  1900
  45
  2200
  400
  ,
  40
  500
  ,
  42
  2
  2
  =
  =
  +
  −
  =
  z
  .  Since 4.85 > 
  1.96, reject Ho and conclude that the two brands differ with respect t