Question

In a survey of 3270 adults aged 57 through 85 years, it was found that 86 9% of them used at least one prescription medication Complete parts (a) through (c) below

a. How many of the 3270 subjects used at least one prescription medication?

b. constuct a 90% interval estimate of the percentage of adults age 57 through 85 years who used at least one prescription medication

round to one decimal place

Answer 1

We know that 86.9% of 3270 adults between 57 and 85 used prescription medication.

a. Thus, the number of subjects who used at least one prescription medication= (3270*86.9)/100

= 2841.63 ~ 2842 subjects.

b. We must build a 90% confidence interval.

Z _0.10/2= Z_0.05= 1.645

Thus, confidence interval=

p_hat - Z * sqrt(p_hat*(1-p_hat)/n) , p_hat + Z * sqrt(p_hat*(1-p_hat)/n)

= 0.869 - 1.645* sqrt(0.869*0.131/3270) , 0.869 + 1.645* sqrt(0.869*0.131/3270)

= 0.869 - 0.009705939 , 0.869 + 0.009705939

= 0.8592941 , 0.8787059~ 85.9% , 87.9%