Help with stats! A poll asked the question, "What do you think is the most important problem facing this country today?" Sixteen percent of the respondents answered "crime and violence." The margin of sampling error was plus or minus 3 percentage points. Following the convention that the margin of error is based on a 95% confidence interval, find a 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters.

Question

Help with stats!  A poll asked the question, "What do you think is the most important problem facing this country today?" Sixteen percent of the respondents answered "crime and violence." The margin of sampling error was plus or minus 3 percentage points. Following the convention that the margin of error is based on a 95% confidence interval, find a 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters.

anonymous · Answer

Not quite sure how to set this one up.

anonymous · Answer

http://books.google.co.in/books?id=kNutPR9P3hoC&pg=PA364&lpg=PA364&dq=A+poll+asked+the+question,+%22What+do+you+think+is+the+most+important+problem+facing+this+country+today?%22+Sixteen+percent+of+the+respondents+answered+%22crime+and+violence.%22+The+margin+of+sampling+error+was+plus+or+minus+3+percentage+points.+Following+the+convention+that+the+margin+of+error+is+based+on+a+95%25+confidence+interval,+find+a+95%25+confidence+interval+for+the+percentage+of+the+population+that+would+respond+%22crime+and+violence%22+to+the+question+asked+by+the+pollsters.&source=bl&ots=EirS9YvfIN&sig=KlZavuHiePHqPEUoDjVPhsA2Gqc&hl=en&sa=X&ei=jbalUavwN4WMrgexloCwAw&ved=0CDMQ6AEwAQ#v=onepage&q=A%20poll%20asked%20the%20question%2C%20%22What%20do%20you%20think%20is%20the%20most%20important%20problem%20facing%20this%20country%20today%3F%22%20Sixteen%20percent%20of%20the%20respondents%20answered%20%22crime%20and%20violence.%22%20The%20margin%20of%20sampling%20error%20was%20plus%20or%20minus%203%20percentage%20points.%20Following%20the%20convention%20that%20the%20margin%20of%20error%20is%20based%20on%20a%2095%25%20confidence%20interval%2C%20find%20a%2095%25%20confidence%20interval%20for%20the%20percentage%20of%20the%20population%20that%20would%20respond%20%22crime%20and%20violence%22%20to%20the%20question%20asked%20by%20the%20pollsters.&f=false

amistre64 · Answer

"What do you think is the most important problem facing this country today?" 

16% of the respondents answered 
        "crime and violence." 

The margin of sampling error was plus or minus 3%

Following the convention that the margin of error is based on a 95% confidence interval, find a 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters.

hmmm, im thinking this looks familiar to me, but ill have to see whats wrong about it first

using .16 as p^ and therefore 1-p^ = q^ = .84
$$\Large .16\pm z_{.95}\sqrt{\frac{.16*.84}{100}}$$

amistre64 · Answer

for starters, Z of (1-95)/2 = Z .025