In a recent poll, 150 people were asked if they liked dogs, and 57% said they did. Find the Margin of Error for this poll, at the 99% confidence level. Give your answer to three decimal places if possible.
Solution :
Given that,
- =57%=0.57
1 - = 1 - 0.57 = 0.43
n=150
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.57
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 2.576 * (((0.57 * 0.43) / 150) = 0.104
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