If a hurricane were 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. com) 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 5,046 adults who live within 20 miles of the coast in high hurricane risk counties of eight southern states. The sample was selected to be representative of the population of coastal residents in these states, so assume that it is reasonable to regard the sample as if it were a random sample.
a. Suppose you are interested in learning about the value of p, the proportion of adults who would refuse to evacuate. This proportion can be estimated using the sample proportion, ˆ p .What is the value of ˆ p for this sample?
b. Based on what you know about the sampling distribution of ˆ p , is it reasonable to think that the estimate is within 0.03 of the actual value of the population proportion? Explain why or why not.