Question

"a survey reports the percentage of people 18 years of age and older who smoke. suppose that a study designed to collect new data on smokers an dnonsmokers uses a preliminary estimate of the proportion that smoke of 0.3. how large a sample should be taken to know with 95% confidence the proportion of smokers within a 0.02 true population proportion"

Answer 1

Answer: 2017

Explanation:

Given : The proportion of people that smoke : p=0.3

Margin of error : E= 0.02

Significance level :
`\alpha=1-0.95=0.05`

Critical value :
`z_(\alpha/2)=1.96`

The formula to calculate sample size ( if proportion is known) :-

`n=p(1-p)((z_(\alpha/2))/(E))^2\\\\\Rightarrow\ n=(0.3)(0.7)(((1.96))/(0.02))\\\\\Rightarrow\ n=2016.84approx2017`

Hence, the required minimum sample would be 2017.