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 .31.

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

Suppose the study showed the proportion of smokers is 0.31., thus the sample proportion assumed as 0.31.

a) At 95% confidence level and margin of error = E= 0.02 the minimum sample is calculated as:

and Zc at 95% confidence level is computed using excel formula for normal distribution which is =NORM.S.INV(0.975) thus Zc at 95% is 1.96.

Now the minimum sample is calculated as:

b) Based on the sample size calculated in part a, and assuming that X= 520 of smokers hence the point estimate is the sample proportion which is calculated as:

c) The Confidence interval is calculated as:

+/- E where E is the margin of error 0.02 thus the confidence inetrval is :

={0.253+/-0.02}

={0.233, 0.273}