Question

1) A school has 1600 students and they are going to vote as to whether they will completely convert the school completely off fossil fuels. How many students would you have to poll to be 95% confident of the outcome within /- 2% of the vote

Answer 1

Answer:

Standard deviation of the students = 0.408

The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote  

         = 0.408 X 1600

         = 652.8    

Step-by-step explanation:  

Step(i):-

Given sample size 'n' = 1600

95% confidence interval of the margin error is determined by

                      $M.E = \frac{Z_{0.05} S.D}{\sqrt{n} }$

Level of significance = 0.05

Z₀.₀₅ = 1.96

Given Margin of error = 2% = 0.02

       $M.E = \frac{Z_{0.05} S.D}{\sqrt{n} }$

       $0.02 = \frac{1.96 X S.D}{\sqrt{1600} }$

      0.02 X √1600 = 1.96 X S.D

       $S.D = \frac{0.02X\sqrt{1600} }{1.96} = 0.408$

Standard deviation of the students = 0.408

The students would you have to poll to be 95% confident of the outcome within /- 2% of the vote  

         = 0.408 X 1600

         = 652.8