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.

Answer 1

Since n=3005 and and population proportion=0.75

The hypotheses are

Rejection region :

Since n>>>30 hence Z test statistic is applicable here as

reject Ho if Z calculated us >Z_0.01=2.33

Test statistic:

P-value:

P-value associated with Z core calculated is computed using the Z table shown below

the p-value is approximately equal to zero.

conclusion:

Since the Z score calculated >>>Z critical at 0.01 level of significance and p-value<<0.01 hence we reject the null hypothesis and conclude that we have enough evidence to support the claim.

The Z table is shown below: