Question

7. The National Survey on Drug Use and Health reported that 4.8% of people aged 12 or older used a prescription pain reliever nonmedically. Suppose that a random sample of 900 people aged 12 or older found that 54 had used a prescription pain reliever nonmedically. Test whether the population proportion has increased, using level of significance ? = 0.01.

Answer 1

Solution:

z test for proportion p

1)

The null and alternative hypothesis are

H₀ : p = 0.048 vs H₁ : p > 0.048

2)

n = 900

x = 54

= 54/900 = 0.06

The test statistic z is

z =  

=  (0.06- 0.048)/[0.048*(1 - 0.048)/900]

= 1.68

3)

Right tailed test

p value = P(Z > 1.68) = 1 - P(Z < 1.68) = 1 - 0.9535 = 0.0465

4)

Since the p value is greater than  level of significance ? = 0.01.,

So , fail to reject H₀

5)

There is not sufficient evidence to support the claim that the population proportion has increased