8.3 Exercise 51

A telephone poll of 1,000 adult Americans was reported in an issue of a national magazine. One of the questions asked, “What is the main problem facing the country?” Twenty percent responded "crime". We are interested in the population proportion of adult Americans who believe that crime is the main problem.

1. Define the random variables X and P′ in words.
2. Which distribution should you use for this problem? Explain your choice.
3. Construct a 95 percent confidence interval for the population proportion of adult Americans who believe that crime is the main problem.
   1. State the confidence interval.
   2. Sketch the graph.
   3. Calculate the error bound.
4. Suppose we want to lower the sampling error. What is one way to accomplish that?
5. The sampling error given by the group of researchers who conducted the poll is ±3 percent. In one to three complete sentences, explain what the ±3 percent represents.