read from a table of X 2 critical values or determined from a calculator. There is a X 2 table in the back of
this book, and you will be supplied a table like this on the AP exam. We will demonstrate both the use of
tables and the calculator in the examples and problems that follow.
A hypothesis test for χ^2 goodness-of-fit follows the by now familiar pattern. The essential parts of the
test are summarized in the following table.
Now, let’s answer the question posed in the opening paragraph of this chapter. We will use the by now
familiar four-step hypothesis-testing procedure introduced in Chapter 11 .
example: The following are the approximate percentages for the different blood types among
white Americans: A: 40%; B: 11%; AB: 4%; O: 45%. A random sample of 1000 black
Americans yielded the following blood type data: A: 270; B: 200; AB: 40; O: 490. Does this
sample indicate that the distribution of blood types among black Americans differs from that of
white Americans?
solution:I . Let p (^) A = proportion of black Americans with type A blood; p (^) B = proportion with type B
blood; p (^) AB = proportion with type AB blood; p (^) O = proportion with type O blood. H 0 : p (^) A
= 0.40, p (^) B = 0.11, p (^) AB = 0.04, p 0 = 0.45.