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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 ā€œUse of Prescription and Over-the-Counter Medications and Dietary Supplements Among Older Adults in the United States,ā€ 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.

Respuesta :

kshemashalet

Answer:

idk

Step-by-step explanation:

MrRoyal

Answer:

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 - Ī± = 0.9,

Ī± = 1 - 0.9

Ī± = 0.1

we need to first determine z(Ī±/2)

z(Ī±/2) = z0.05

From z-score table

z0.05 = 1.645

Then we calculate the margin of error using

E = z(Ī±/2) * āˆš(pq/n)

If p = 81.7% = 0.817

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

So, E = 1.645 * āˆš(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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