SOLUTION: A recent poll of 700 people who work indoors found that 278 of them smoke. If the researchers want to be 98% confident of their results to within 3.5%, how large a sample is necess

Question 1040402: A recent poll of 700 people who work indoors found that 278 of them smoke. If the researchers want to be 98% confident of their results to within 3.5%, how large a sample is necessary?
A.
532
B.
1301
C.
1062
D.
751

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
278/700=0.397
CI for 1 sample proportion =0.035 here, and that is z (0.99)sqrt { (p)(1-p)/n}; square both sides
0.035^2=0.001225=z^2(0.99)*p*(1-p)/n
z(0.99)=2.326
0.001225=5.410*(.397)(.603)/n; now multiply both sides by n then divide both by 0.001225
n=5.410*(.397)(.603)/0.001225=1057. Within rounding error, C would be the choice.
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