1 answer

The Centers for Disease Control reported the percentage of people 18 years of age and older...

Question:

The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December
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 27. a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (rounded up to the next 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)?

Answers

solution:-

a. given that margin of error E = 0.02 , p = 0.27

the value of 95% confidence from z table is 1.96

sample size formula

=> n = p* (1-p)*(z/E)^2

=> n = 0.27*(1-0.27)*(1.96/0.02)^2

=> n = 1893

b. here given that x = 520

then proportion p = x/n = 520/1893 = 0.2745

c.confidence interval

the value of 95% confidence level is 1.96

formula

=> p +/- z * sqrt(p*(1-p)/n)

=> 0.2745 +/- 1.96 * sqrt(0.2745*(1-0.2745)/1893)

=> (0.2544 , 0.2946)


.

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