You wish to conduct a survey in your city to determine what percent of the bicyclists own helmets. Find the sample size if you want your estimate to be within a margin of error 3% with 95% confidence.
Solution :
Given that,
= 0.5
1 - = 1 - 0.5= 0.5
margin of error = E = 3% = 0.03
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96 ( Using z table )
Sample size = n = (Z/2 / E)2 * * (1 - )
= (1.96 / 0.03)2 * 0.5 * 0.5
= 1067.1111
Sample size =1068
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