Question

The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .29.

a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)? Use 95% confidence.

b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?

c. What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)?

( ,  )

Answer 1

a)

Sample size = Z²/2 * p( 1 - p) / E²

= 1.96² * 0.29 * 0.71 / 0.02²

= 1977.46

n = 1978 (Rounded up to nearest integer)

b)

Point estimate of proportion = 520 / 1978 = 0.263

c)

95% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.263 - 1.96 * sqrt( 0.263 * 0.737 / 1978) < p < 0.263 + 1.96 * sqrt( 0.263 * 0.737 / 1978)

0.244 < p < 0.282

95% CI is ( 0.2436 , 0.2824 )