Question

In a survey of 3005 adults aged 57 through 85 years, it was found that 81.7% of the 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)
a. How many of the 3005 subjects used at least one prescription medication?

b. Construct a 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication.

Answer 1

Do you need help with a. ?

Answer 2

yes

Answer 3

a. The number of subjects that used a least one prescription medicine is given by:
\[\frac{3005\times81.7}{100}=you\ can\ calculate\]

Answer 4

2455.085

Answer 5

Correct, when rounded to 2455.

Answer 6

ok can you please help me with b

Answer 7

b. The sample mean = np = 3005 * .871 = 2455
The standard deviation is found from:
\[\sqrt{np(1-p)}=\sqrt{2455\times0.183}=21.19\]
The margin of error is:
\[1.645\times\frac{21.19}{\sqrt{3005}}=0.636\]
Rounding, we get the confidence interval for the sample mean as: (2454, 2456).
Therefore the confidence interval estimate for the percentage who use at least on prescription medication is:
\[(\frac{2454}{3005}\times100,\ \frac{2456}{3005}\times100)=\]
(81.66%, 81.73%)