Data in 1980 showed that about 42% of one country's population had never smoked cigarettes.In 2004,a national health survey in this country interviewed a random sample of 3000 adults and found that 51% had never been smokers.Create a 95% confidence interval for the proportion in 2004 of this country's adults who had never been smokers.

A) Based on the data,we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 49.2% and 52.8%.
B) Based on the data,we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 47.8% and 58.2%.
C) Based on the data,we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 49.2% and 63.2%.
D) Based on the data,we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 40% and 60%.
E) Based on the data,we are 95% confident the proportion of adults in 2004 who had never smoked cigarettes is between 37.4% and 52.8%.

Question

Moses Kabineh · Accepted Answer

Final Answer : A, Explanation :   The 95% confidence interval for a proportion is calculated using the formula:   p ± z p ( 1 − p ) n p \pm z\sqrt{\frac{p(1-p)}{n}} p ± z n p ( 1 − p ) ​ ​  , where   p p p   is the sample proportion,   z z z   is the z-score for the desired confidence level (approximately 1.96 for 95%), and   n n n   is the sample size. Plugging in the values:   0.51 ± 1.96 0.51 ( 1 − 0.51 ) 3000 0.51 \pm 1.96\sqrt{\frac{0.51(1-0.51)}{3000}} 0.51 ± 1.96 3000 0.51 ( 1 − 0.51 ) ​ ​   gives an interval of approximately   0.492 0.492 0.492   to   0.528 0.528 0.528   or 49.2% to 52.8%.

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