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 6138 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.)
(  ,   )

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.34

1 - = 0.66

Z_/2 = 2.326

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.326 * (((0.34 * 0.66) / 6138)

= 0.014

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.34 - 0.014 < p < 0.34 + 0.014

0.326 < p < 0.354

The 98% confidence interval for the population proportion p is : (0.326 , 0.354)