Question

Consider a simple poll that is measuring the proportion of citizens that hold a particular political belief. What is a conservative, "worst case scenario" sample size if you want the margin of error to be 5.8%?

Answer 1

Solution:

Given:

Margin of Error =5.8% = 0.058

Confidence level is not given, so we assume c = 95% confidence level

p = proportion of citizens that hold a particular political belief is unknown

so we assume p = 0.5

Formula:

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus