Basic Statistics

SINGLE POPULATION PROPORTION 127

Figure 10.1 Pie chart of proportion of successes and complications.

Figure 10.2 Bar chart of counts of complications and successes.

In pie or bar charts either counts, proportions, or percents can be displayed. Fig-
ure 10.2 displays the outcome as counts; there were 15 successes and 5 failures.
The population mean of the young patients was the number of successes divided
by the number of patients in the population or 7r and is equal to 15/20 = .75. The
population variance can be shown to be 7r(1 - T), or .75(1 - .75) = .1878.
The number T is a population parameter, just as are p and 0; pis the corresponding
sample statistic. The parameter p and its estimate x were studied in Section 5.3 by
computing a large number of x’s. This led to a study of the distribution of x’s.
Then, in Chapter 7 confidence intervals were constructed for p (and also for p1 - p2
in the case of two populations). Finally, in Chapter 8, tests of hypotheses were made
concerning p (and concerning 1-11 = p~).
In this chapter, the distribution of p is considered, and the same confidence intervals
and tests of significance will be developed for T as were developed earlier for p. This