534 



APPENDIX 



A.31. An experimenl is performed four 

 times. X is 5, 7. 10. and 1 1 when N 

 is 8, 20, 20, 30, respectively. Are all 

 tour results mutually consistent? 



A.32. Suppose the label on two packages 

 of grass seed states that each package 

 will germinate 40% grass type A, 

 35* J grass type B, 15% grass type C, 

 .iiul It)' J weeds D. A sample from 

 package 1 germinates 400A, 400B, 

 50C, and 150D. A sample from 

 package 2 yields 390A, 410B, 70C, 

 and 130D. Compare the contents 

 of each package with the labelled 

 contents and with each other. What 

 do you conclude? 



A drug manufacturer receives results 

 of using or not using his product. 

 As a check on bias in testing he scores 

 the control and experimental group 

 for eye color and ABO blood type 

 and finds the results tabulated below. 



AB A 



A. 33. 



Blue Brown 

 Control 7 6 



Experimental 4 8 



B 



Blue Brown 

 Control 4 4 



Experimental 5 2 



Blue Brown 

 8 9 



8 12 



What should he conclude about bias? 

 A. 34. Suppose women were classified in 

 two ways: hair color and tempera- 

 ment. I sing the results listed be- 

 low, test the hypothesis that there is 

 no relation between hair color and 

 temperament. 



figure A-6. The normal curve. 



III. INDISCRETE VARIABLES 



A. Parameters and the Normal Curve 



Suppose a particular measurement is the 

 result of the action of a very large number 

 of independent variables, each of which has 

 approximately the same magnitude of effect 

 on the measurement. If, then, an infinitely 

 large number of such measurements are 

 collected, they will be expected to have a 

 range of values which are said to be nor- 

 mally distributed. Figure A-6 shows the 

 normal distribution or curve formed by 

 plotting these measurements against the 

 frequency with which they would be ex- 

 pected to occur in this infinitely large popu- 

 lation. The population mean, or "true" 

 mean, is denoted by the parameter n. The 

 population standard deviation, or "true" 

 standard deviation, is represented by the 

 lower case Greek letter sigma, a. It is 

 known that about % of all the measure- 

 ments in a normal curve lie within one a 

 of the mean, and about 95% of all measure- 

 ments lie within 2 a of the mean (being in 

 the range n ± 2 a). Strictly speaking, the 

 individual "measurements" or values which 

 comprise the normal curve are also pa- 

 rameters. 



The normal curve vs. the binomial dis- 

 tribution. Suppose N = 20 and p = 3 / 6- 

 If an infinitely large number of samples 



