EXAMPLE 7 Sign test for binomial data

The National Center for Health Statistics reports that 50% of Americans take at least one prescription drug per month. Suppose that a random sample of 100 Americans shows 67 who took at least one prescription drug per month. Test whether the proportion of Americans who take at least one prescription drug per month has increased, using .

Solution

Because the sample of Americans has been selected randomly and , we may proceed. We represent people taking at least one prescription drug per month by plus (+) signs and people taking no prescription drugs by minus (–) signs.

  • Step 1 State the hypotheses.

    where represents the population proportion of Americans taking at least one prescription drug per month.

  • Step 2 Find the critical value and state the rejection rule. The sample size is greater than 25, so we may use the large-sample case. Using Table 4 in Chapter 9 (page 500) for level of significance , we have . We will reject if .
  • Step 3 Find the value of the test statistic. From Table 5, . Thus, . We then calculate the test statistic :

  • Step 4 State the conclusion and the interpretation. Because is , we reject . Evidence exists that the population proportion of Americans taking at least one prescription drug per month has increased.

NOW YOU CAN DO

Exercises 25–26.