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.

a. The number of people that used at least one prescription is 2,455.

b. We're 90% confident that the true percentage of adults aged 57 to 85 that use at least one prescription is between 80.54% and 82.86%

Step-by-step explanation:

Given

Sample Size = S = 3005

Percentage of those that used at least one prescription = p = 81.7%

a. Number of the 3005 subjects used at least one prescription medication is calculated by multiplying the percentage by total.

i.e 81.7% * 3005

= 2,455.085

= 2,455 --- Approximated.

Hence, the number of people that used at least one prescription is 2,455.

b. Using a confidence level of 90%

c = 90%

Using 1 - α = 0.9,

α = 1 - 0.9

α = 0.1

we need to first determine z(α/2)

z(α/2) = z0.05

From z-score table

z0.05 = 1.645

Then we calculate the margin of error using

E = z(α/2) * √(pq/n)

If p = 81.7% = 0.817

Where q = 1 - p = 1 - 0.817 = 0.183

So, E = 1.645 * √(0.817 * 0.183/3005)

E = 0.011603265702668

E = 0.0116

Then we calculate the boundaries of the confidence Interval using

p - E and p + E

p - E = 0.817 - 0.0116 = 0.8054 = 80.54%

p + E = 0.817 + 0.0116 = 0.8286 = 82.86%

We're 90% confident that the true percentage of adults aged 57 to 85 that use at least one prescription is between 80.54% and 82.86%

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