CHAPTER 6 



Introductory Sampling Theory 

 for a Normal Population 

 Involving Only One Variable 



When the population being sampled has a normal frequency dis- 

 tribution with unknown parameters fj. and a, the problems of estima- 

 tion and of testing hypotheses by means of samples are fundamentally 

 much the same as those considered in Chapter 5 for binomial pop- 

 ulations. Two differences are immediately apparent, (a) There now 

 are two unknown parameters instead of one, as for the binomial pop- 

 ulation, and (6) the measurements, A", have a continuous scale of 

 measurement and a continuous frequency distribution. These dif- 

 ferences between the normal and the binomial types of populations 

 will appear in the discussions below as the causes of some changes 

 in the mechanics of estimation and of testing hypotheses; but the 

 reader should not lose sight of the fact that the problems and their 

 solutions are much the same as in Chapter 5. 



6.1 OBTAINING THE SAMPLE 



The process for obtaining good samples from a normal population 

 is similar to that discussed in Chapter 5 for randomization and the 

 avoidance of biases. Here, as there, the population to be sampled 

 must be clearly defined, and the measurement to be taken on the 

 units of this population must be stipulated precisely. 



After the population is specified and the units (persons, prices, 

 pigs, plots of land, pots of plants, families, etc.) have been designated 

 unambiguously, it is necessary to devise a method for obtaining the 

 particular units which are to constitute the sample. The sampling 

 situations which come within the scope of this chapter should be 

 handled by completely randomized samples. To illustrate, suppose 

 that a person who is interested in the production of raw rubber wishes 



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