SOLUTION: A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 wi

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Question 1157233: A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 90​% confidence if
​(a) she uses a previous estimate of 0.32​?
​(b) she does not use any prior​ estimates?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
90% CI is z*SE=0.04 for half-interval
so 1.645*sqrt(.32*.68/n)=0.04
and
1.645*sqrt(.32*.68)/0.04=sqrt(n)
square both sides
n=368.02 or 369 rounding up
when the estimates are unknown, use .5 as the most conservative
1.645*sqrt*(.25)/0.04=sqrt (n)'
n=422.8 or 423
having a prior estimate that is further from 0.5 in either direction will lower the needed sample size.