Question

In a survey of 3314 adults aged 57 through 85​ years, it was found that 82.7% of them used at least one prescription medication. Complete parts​ (a) through​ (c) below. a. How many of the

3314 subjects used at least one prescription​ medication?

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

______​%< p<_____%

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

Answer 1

a.

The number of subjects who used at least one prescription​ medication =3314*82.7% =2,740.678. Since the number of subjects cannot be a fraction, it is 2741.​​​​​​

b.

Sample proportion, =82.7% =0.827

Sample size, n =3314

np =3314*0.827 =2741

n(1-p) =3314(1-0.827) =573

Standard Error, SE = = =0.0066

At 90% confidence level, for a two-tailed case, Z_critical =1.645

Margin of Error, MoE =Z_critical*SE =1.645*0.0066 =0.0108

90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication is: p =MoE =0.827 0.0108 =(0.8162, 0.8378) =(81.6%, 83.8%). (rounded to one decimal place).