Question

in a survey of 3429 adults aged 57 through 85 years it was found that 85.8% of them used at least one prescription medication.

a. How many of the 3429 used at least one prescription mediaction?

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

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

Answer 1

a)
expected number = 3429 * 0.858 = 2942.082
i.e. 2942

b)
sample proportion, = 0.858
sample size, n = 3429
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.858 * (1 - 0.858)/3429) = 0.006

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.858 - 1.64 * 0.006 , 0.858 + 1.64 * 0.006)
CI = (0.8482 , 0.8678)

c)
We are 90% confident that the true population proportion of adults who used at least one prescription medication is between (0.8482 , 0.8678)