Question

In a survey of 3413 adults aged 57 through 85​ years, it was found that 85.6​% of them used at least one prescription medication. Complete parts​ (a) through​ (c) below.

a. How many of the subjects used at least one prescription​ medication?

​(Round to the nearest integer as​ needed.)

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

nothing​%less than<pless than<nothing​%

​(Round to one decimal place as​ needed.)

c. What do the results tell us about the proportion of college students who use at least one prescription​ medication?

Answer 1

Answer:

a)

Given,

n = 3413

p = 0.85

To give the number of subjects used at least one prescription medication

i.e.,

= np

substitute values

= 3413*0.85

The number of subjects used at least one prescription medication = 2901

b)

Here z value for 90% confidence interval is 1.645

To construct the 90% confidence interval

i.e.,

= (p^ - z*sqrt(p^(1-p^)/n)) < p <  (p^ + z*sqrt(p^(1-p^)/n))

substitute the values known

= (0.85 - 1.645*sqrt(0.85(1-0.85)/3413)) < p < (0.85 + 1.645*sqrt(0.85(1-0.85)/3413))

= (0.85 - 0.0101 < p < 0.85 + 0.0101)

= (0.8399 < p < 0.8601)

CI = 84.0% < p < 86.0%

c)

Here we can say that the result observed in (b) tells that the results tell us about the proportion of college students who use at least one prescription​ medication is found in the above part (b) i.e., 90% confidence