Question

In a survey of 3005 adults aged 57 through 85 years, it was found that 81.7% of them used at least one prescription medication (based on data from “Use of Prescription and Over-the-Counter Medications and Dietary Supplements Among Older Adults in the United States,” by Qato et al., Journal of the American Medical Association, Vol. 300, No. 24). Use a 0.01 significance level to test the claim that more than 3/4 of adults use at least one prescription medication. Does the rate of prescription use among adults appear to be high?

Answer 1

Let the proportion, p = adults who used at least one prescription medication

The z test for the one proportion is used since the sample data values satisfy the normality condition

The null and alternative hypotheses are defined as,

The z-statistic is obtained using the formula,

The p-value is obtained from the z-distribution table for z = 8.478

Since the P-value is 0.0000<0.01 at 1% significant level, the null hypothesis is rejected. Hence we can conclude that more than 3/4 of adults use at least one prescription medication