9.34 A. C. Nielsen Co. has electronic monitors hooked up to about 1,200 of the 80 million American homes. The data from the monitors provide estimates of the proportion of homes tuned to a particular TV program. Nielsen offers the following defense of this sample size:

Mix together 70,000 white beans and 30,000 red beans and then scoop out a sample of 1,000. The mathematical odds are that the number of red beans will be between 270 and 330, or 27 to 33 percent of the sample, which translates to a “rating” of 30, plus or minus three, with a 20 to 1 assurance of statistical reliability. The basic statistical law wouldn’t change even if the sampling came from 80 million beans rather than 100,000 (Sky, October 1982).
Interpret and justify this statement in terms of the results of this chapter.