The general practice in making preelection polls is to use a

The general practice in making pre-election polls is to use about 1000 responses. Statistics theory predicts that the standard deviation for N responses is the square root of N. What is the standard error for this number of responses? What is the relative uncertainty expressed as a percentage of the total responses? Why do pollsters use about 1000 responses?

Solution

Suppose that x is a random variable representing number of pre-election polls that follows poisson distribution

we are given that standard deviation of number of pre-election polls = square root(1000)

and we know that mean and variance of normal distribution is same. Thus variance and mean of number of polls is 1000.

Now

a) standard error is = standard deviation / square root of 1000

= square root of 1000 / square root of 1000

=1

b) relative error = uncertainity of (x) / measured quantity

uncertanity of x= standard error of (x)

m = measured quantity +- uncertanity of x

m = mean(x) +- standard error of (x)

= 1000 +- 1

thus relative error = 1/ 1000

= 0.001

Why pollsters use 1000 responses:

The pollsters use large number of responses because accuracy of results incerases by increasing the number of responses.