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 .34.

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)

p= 0.34, E= 0.02, C= 95%

Formula for sample size is

Where Zc is the Z critical value for the C= 95%

Zc= 1.96

n = 2155.1376

sample size required = 2156

b) x= 520, n= 2156

formula for point estimate is

point estimate is = 0.2412

c)

formula for confidence interval is

Where Zc is the Z critical value for the C= 95%

Zc= 1.96

0.22313 < P < 0.25925

Confidence interval is = ( 0.2231 , 0.2593 )