If a hurricane was headed your way, would you evacuate? the headline of a press release issued january 21, 2009 by the survey research company international communications research (icrsurvey) states, "thirty- one percent of people on high-risk coast will refuse evacuation order, survey of hurricane preparedness finds." this headline was based on a survey of 5046 adults who live within 20 miles of the coast in high hur- ricane 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 resi- dents in these states.
use this information to estimate the proportion of coastal residents who would evacuate using a 98% confidence interval.
write a few sentences interpreting the interval and the confidence level assosiated with the interval.

The 98% confidence interval for population proportion of people who refuse evacuation is {0.30, 0.33].

Step-by-step explanation:

The sample drawn is of size, n = 5046.

As the sample size is large, i.e. n > 30, according to the Central limit theorem the sampling distribution of sample proportion will be normally distributed with mean and standard deviation .

The mean is:

The confidence level (CL) = 98%

The confidence interval for single proportion is:

Here = critical value and α = significance level.

Compute the value of α as follows:

For α = 0.02 the critical value can be computed from the z table.

Then the value of is ± 2.33.

The 98% confidence interval for population proportion is:

Thus, the 98% confidence interval [0.30, 0.33] implies that there is a 0.98 probability that the population proportion of people who refuse evacuation is between 0.30 and 0.33.