Question

3.         A random sample of 2000 adults was selected in order to estimate the proportion of the population that has received at least one college degree.

864 of the 2000 adults responded that they have received at least one college degree.

Determine the 99% confidence interval for the proportion of the population that has received at least one college degree.

Then complete the sentence provided below:

           With 99% confidence the proportion of the population that has received at least one college degree is between _________________ and __________________ .

Answer 1

sample proportion, = 0.432
sample size, n = 2000
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.432 * (1 - 0.432)/2000) = 0.0111

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

Margin of Error, ME = zc * SE
ME = 2.58 * 0.0111
ME = 0.0286

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.432 - 2.58 * 0.0111 , 0.432 + 2.58 * 0.0111)
CI = (0.4034 , 0.4606)

With 99% confidence the proportion of the population that has received at least one college degree is between 0.4034 and 0.4606