In: Statistics and Probability
Tom Nook would like to launch an investigation to see what proportion of fish caught are horse mackerals. What sample size would be required to do this with 95% confidence to within 0.03?
Solution :
Given that,
= 0.5
1 - = 1 - 0.5 = 0.5
margin of error = E = 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
= 1067.11
Sample size =1067