Question

ccording to the Center for Disease Control, the prevalence of smoking among adults in Oregon is 16.3%. It is 20.5% in Louisiana. In both states, theses estimates are based on samples of 1000 adults. What is the standard error for each state

Answer 1

SE = 0.01730335

Explanation:

We have two independent population (smokers in Oregon and Smokers in Louisiana).

Proportion of smokers (adult) in Oregon (Po) = 0.163

Proportion of non-smokers (adult) in Oregon (1- Po) = 0.837

Proportion of smokers (adult) in Louisiana (Ps) = 0.205

Proportion of non-smokers (adult) in Louisiana (1- Ps) = 0.795

With equal sample sizes (n) selected ==> no and ns = 1000.

Where no represents the sample size taken in Oregon and ns represents the sample size taken in Louisiana.

By Standard Error (SE) =
`\sqrt{(Po(1-Po) + Ps(1-Ps))/(n) }` ; the n implies equal sample size.

Therefore;

SE =
`\sqrt{((0.163*0.837) + (0.205*0.795))/(1000)}` = 0.01730335