Question

A telephone poll of 1,000 adult Americans was reported in an issue of Time Magazine. One of the questions asked was “What is the main problem facing the country?” Twenty percent answered “crime.” We are interested in the population proportion of adult Americans who feel that crime is the main problem.

a. Sketch the graph.

b. Calculate the error bound.
c. Suppose we want to lower the sampling error. What is one way to accomplish that?

d. The sampling error given by Yankelovich Partners, Inc. (which conducted the poll) is ±3%. In one to three complete sentences, explain what the ±3% represents.

Answer 1

a. A bar graph for the given data is shown below:

1250 1000 1000 o 750 500 250 200 People who think crime is main problem People who think otherwise Problems facing the countryy meta-chart.com
b. Since this a binomial population, where p is our sample proportion (p=0.2) the error bound is given by e=1.96x$\sqrt{p(1-p)/n}$, e = 0.025, therefore our sample proportion estimate will be 0.2 ± 0.025. This is with respect to 95% level of confidence(hence the value 1.96). Also we are able to use the z-score as the minimum sample size is also met with respect to given sample proportion.

c. One way to reduce the sampling error is to increase our sample size, basically take more people into account for the survey.

d. What this means is:

Say our confidence level was 95%, then we can say that we are 95% confident that 20% ± 3% of all adult Americans think that crime is the main problem facing the country