Question

You are working for a certain candidate who is running a provincial election. This candidate finds out that you have taken a statistics course from a certain statistics professor, and assumes that you know a bit about statistics and sampling. The candidate asks you to take a poll in order to estimate the proportion of the voters who cast their vote for him/her with a margin of error of 0.035. You take it upon yourself to take a simple random sample of voters. How many samples do you need for a 90% confidence interval. Assume that a recent survey showed 47% of voters have supported him/her.

Answer 1

Solution :

Given that,

= 47%=0.47

1 - = 1 - 0.47= 0.53

margin of error = E = 0.035

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table ( see the 0.05 value in standard normal (z) table corresponding z value is 1.645 )   

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.645 / 0.035)2 * 0.47 * 0.53

=550.26

Sample size = 551 ( APPROXIMATLEY ROUNDED)