Introduction to Probability and Statistics for Engineers and Scientists

518 Chapter 12:Nonparametric Hypothesis Tests

area = 1/2

m

area > 1/2

m m 0

area < 1/2

m 0 m

FIGURE 12.1

resultingp-value is the probability that a value ofvor smaller would have occurred by
chance if each element had probability 1/2 of being less thanm 0. That is,

p-value=P{Bin(n, 1/2)≤v}

EXAMPLE 12.2b A financial institution has decided to open an office in a certain commu-
nity if it can be established that the median annual income of families in the community is
greater than $90,000. To obtain information, a random sample of 80 families was chosen,
and the family incomes determined. If 28 of these families had annual incomes below
and 52 had annual incomes above $90,000, is this significant enough to establish, say, at
the 5 percent level of significance, that the median annual income in the community is
greater than $90,000?

SOLUTION We need to see if the data are sufficient to enable us to reject the null hypothesis
when testing

H 0 :m≤90 versus H 1 :m> 90

The preceding is equivalent to testing

H 0 :p≥1/2 versus H 1 :p<1/2