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"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"

Respuesta :

JeanaShupp

Answer: 2017

Step-by-step explanation:

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

Margin of error : E= 0.02

Significance level :[tex]\alpha=1-0.95=0.05[/tex]

Critical value : [tex]z_{\alpha/2}=1.96[/tex]

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

[tex]n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\\Rightarrow\ n=(0.3)(0.7)(\dfrac{(1.96)}{0.02})\\\\\Rightarrow\ n=2016.84approx2017[/tex]

Hence, the required minimum sample would be 2017.

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