6.2 – Medication Usage. In a survey of 3005 adults aged 57 through 85 years, it
ID: 3129699 • Letter: 6
Question
6.2 – Medication Usage. 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-theCounter Medications and Dietary Supplements Among Older Adults in the United State,” by Qato et al., Journal of American Medical Association, Vol. 300, No. 24).
a) How many of the 3005 subjects used at prescription medication? We are given that out of n = 3005 subjects, proportion p = 0.817 used at least one prescription medication. Calculate the number of people who used at least one prescription medication in the sample using formula x = pn.
b) Construct a 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication. We have n = 3005, x (from part a), and confidence level c = 0.9.
c) What do the results tell us about the proportion of college students who use at least one prescription medication?
Explanation / Answer
a)
x = n p = 3005*0.817 = 2455 [ANSWER]
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b)
Note that
p^ = point estimate of the population proportion = x / n = 0.816971714
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.00705408
Now, for the critical z,
alpha/2 = 0.05
Thus, z(alpha/2) = 1.644853627
Thus,
Margin of error = z(alpha/2)*sp = 0.011602929
lower bound = p^ - z(alpha/2) * sp = 0.805368785
upper bound = p^ + z(alpha/2) * sp = 0.828574643
Thus, the confidence interval is
( 0.805368785 , 0.828574643 ) [ANSWER]
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c)
We are 90% confident that the proportion of college students who use at least one prescription medication is between 0.80537 and 0.82857.
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