Question

A telephone poll of 1000 adult Americans was reported in a magazine. One of the questions asked was "What is the main problem facing the country?" Suppose 18% answered "crime". We are interested in the population proportion of adult Americans who feel that crime is the main problem.

NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Construct a 95% confidence interval for the population proportion of adult Americans who feel that crime is the main problem.

(i) State the confidence interval. (Round your answers to four decimal places.)

(iii) Calculate the error bound. (Round your answer to four decimal places.)

Answer 1

(i)

Sample proportion, p = 0.18

np(1-p) = 1000 * 0.18 * (1 - 0.18) = 147.6

Since np(1-p) > 10, the sample size is large enough to approximate the sampling distribution of proportions as normal distribution.

Z score for confidence interval is 1.96

Standard error of proportion, SE = = 0.01214907

Margin of error = Z * SE = 1.96 * 0.01214907 = 0.0238

95% confidence interval for the population proportion of adult Americans who feel that crime is the main problem is,

(0.18 - 0.0238 ,  0.18 + 0.0238)

(0.1562 ,  0.2038)

(ii)

Error bound = Margin of error = 0.0238