Question

If a hurricane was headed your way, would you evacuate? The headline of a press release states, "Thirty-four Percent of People on High-Risk Coast Will Refuse Evacuation Order, Survey of Hurricane Preparedness Finds." This headline was based on a survey of 6627 adults who live within 20 miles of the coast in high hurricane risk counties of eight southern states. In selecting the sample, care was taken to ensure that the sample would be representative of the population of coastal residents in these states.

(a) Use this information to estimate the proportion of coastal residents who would evacuate using a 98% confidence interval. (Round your answers to three decimal places.)
(  ,  )

(b) Write a few sentences interpreting the interval and the confidence level associated with the interval.

We are  % confident that the proportion of all coastal residents who  ---Select--- would would not evacuate is within the confidence interval. If we were to take a large number of random samples of size 6627,  % of the resulting confidence intervals would contain the true proportion of all coastal residents who  ---Select--- would would not evacuate.

Answer 1

a)
sample proportion, pcap = 0.34
sample size, n = 6627
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.34 * (1 - 0.34)/6627) = 0.0058

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, Zc = Z(α/2) = 2.33

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.34 - 2.33 * 0.0058 , 0.34 + 2.33 * 0.0058)
CI = (0.326 , 0.354)

b)
We are 98% confident that the proportion of all coastal residents who would evacuate is within the confidence interval.

If we were to take a large number of random samples of size 6627, 98% of the resulting confidence intervals would contain the true proportion of all coastal residents who would evacuate.