Sec. 5.2 POINT AND INTERVAL ESTIMATION OF p 121 



(b) As in a, but have one laboratory test all one company's beams, the sec- 

 ond laboratory testing all the second company's beams. 



(c) Go into the public market and purchase the necessary number of beams 

 of each type, and then do as in a. 



(d) As in c, but replace a by b. 



(e) Specify other ways. 



6. An agronomist wishes to run critical yield, protein, and test weight studies 

 on a proposed new variety of wheat before the variety is released to the public. 

 He proposes to use a standard and widely planted variety for comparison with 

 the new one. Plenty of land is available for this study, but it is quite non- 

 uniform in soil qualities, moisture content, and exposure to weather. Which 

 of the following outlines for such a study would you prefer, and why? 



(a) Plant the new variety on the east half of the available land, the standard 

 variety on the west half (or vice versa, as decided by flipping a coin), harvest 

 and measure wheat from each half, determine test weight and protein content 

 on the yield from each half separately. 



(b) Divide the available area into 20 equal-sized plots and plant 10 plots to 

 each variety, choosing the variety for a plot by drawing the names from a hat. 

 Then determine yield, protein, and test weight separately from each plot's 

 wheat. 



(c) Do as in b, except that the plots are grouped into 10 pairs and each pair 

 has both varieties planted side by side. 



(d) Save the land for some other purpose, send out samples of each wheat 

 to 10 farmers, and ask them to report the yields and test weights and send in 

 samples for protein analysis. 



5.2 CALCULATION OF POINT AND INTERVAL ESTI- 

 MATES OF p FOR A BINOMIAL POPULATION 



It was indicated in Chapter 4 that a binomial frequency distribu- 

 tion can be defined when individuals are identified only as belonging 

 to one of two possible classes of attributes such as male or female, 

 dead or alive, acceptable product or unacceptable product, and the 

 like. Moreover, the proportions falling into the two classes of at- 

 tributes are constantly p: (1 — p). 



If n members of a binomial population are selected at random, 

 the particular individuals drawn are the result of chance occurrences. 

 Hence, we may find that any number from r = to r = n of those 

 individuals possess the attribute A, say, even though a fixed propor- 

 tion, p, have that attribute in the whole population. The possible 

 outcomes of such a sampling vary from r = to r = n and form a 

 binomial frequency distribution with mean /a = np and with standard 

 deviation o- = y/npq, as was shown in Chapter 4. The reader is 

 reminded that the probability that exactly r of the n members of 



