140 SAMPLING FROM BINOMIAL POPULATIONS Ch. 5 



6. Samples from records of male and female White Rock chicks up to 8 

 weeks of age raised at Kansas State College during 1945 gave the following data: 



Sex Died Lived 



Male 46 227 



Female 30 290 



Use the x 2- test to decide if there probably is a fundamental difference in chick 

 mortality due to sex. Arts. P( x 2 — 7.35) =.007. 



7. The following data are derived from a publication by Atkeson et al. (Jour- 

 nal oj Economic Entomology, 37:428-35) on the effectiveness of 5 sprays in 

 killing flies around dairy barns: 



Number of Flies 



Spray Killed Not Killed 



Which sprays do you consider as essentially equal in killing power, considering 

 sprays which do not differ beyond reasonable sampling variation as being tied? 



5.5 THE X 2 -TEST WHEN MORE THAN ONE DEGREE 

 OF FREEDOM IS REQUIRED 



There are many problems in sampling which require the use of 

 the sampling distribution of a x 2 with more than one degree of free- 

 dom, but only a few will be considered in this book. For example, 

 suppose that both parents have the specific blood types AO and 

 Rhrh, in the symbols of Chapter 3. Each parent produces four types 

 of gametes: ARh, Arh, ORh, and Orh, with equal frequencies it is 

 believed. Hence it can be deduced that such parents will produce 

 offspring of four blood types: ARh + , ARh — , ORh + , and ORh—, 

 with associated probabilities 9/16, 3/16, 3/16, and 1/16, respectively. 

 Therefore, if a large number of such parents is obtained for a random 

 sample we can test the hypothesis suggested by the above argument, 

 namely, H (9 ARh+ : 3 ARh- : 3 ORh+ : 1 ORh-). To illus- 

 trate, suppose that out of 1600 such families in a random sample, the 

 children were classified as follows with respect to the A-B and Rh 

 blood groups: 885 ARh+, 310 ARh-, 292 ORh+, and 113 ORh-. 

 Do these observed numbers deviate enough from the corresponding 



