154 SAMPLING NORMAL POPULATIONS Ch. 6 



to estimate the percentage rubber in a certain variety of guayule 

 grown under specified environmental conditions. Suppose also that 

 he wishes to select and to analyze 25 plants as a basis for this esti- 

 mate. The population parameter which is to be estimated is the true 

 average percentage of rubber in plants of the given variety. Assum- 

 ing that there is a large number of guayule plants from which to 

 select a sample, how should the particular 25 of the sample be chosen? 

 If the 25 tallest, sturdiest, or most thrifty-looking plants were to be 

 chosen they surely would not be representative of the population. 

 If a person were to stroll about among the available plants and choose 

 25 in what he considered a random manner, he might unconsciously 

 bias the sample. A better way to choose the sample is to assign 

 location numbers (such as row and plant-in-row numbers) to the 

 plants and then effectively "just draw 25 numbers out of a hat." He 

 can use tables of random numbers and similar devices if he chooses. 

 The main point is to see that every plant in the population had at 

 the start an equal and independent chance to be included in the 

 sample. 



If two varieties of guayule were compared for percentage of rub- 

 ber, it might be best to start with a suitable area of land staked off 

 for tree spacings and then assign the varieties at random to the 

 various planting positions. This would make it true that each 

 variety initially had an equal chance for any good, or bad, land 

 among the possible planting positions. 



The subject of this section is very broad and complex partly be- 

 cause there are many different sampling situations and a consequent 

 need to devise different sampling procedures to fit these different cir- 

 cumstances. However, as in Chapter 5, only enough is said here to 

 give the reader some general ideas and, perhaps, induce him to do 

 more reading on this subject if he is interested. At the least, the 

 reader can be critical in accepting sampling results presented as 

 information, advertising, or propaganda. 



6.2 THE STATISTICAL DISTRIBUTION OF SAMPLE 

 MEANS, x„ DRAWN FROM A NORMAL POPULATION 



Each sample drawn from a normal population of numerical meas- 

 urements will nearly always differ from any other sample from the 

 same population in one or more details. Yet certain features of 

 samples from a population, as a group, will tend to conform to a 

 predictable pattern. For example, if 10 observations are to be taken 



