You work as a consultant who provides polling for various political campaigns. One of your clients is a mayoral candidate in the State of Virginia. The election is a few weeks away, and the candidate is getting nervous about his chances to win re-election. He asks you to do another poll to determine his next move (more paid ads, canvassing, etc.) As a pollster, you want to provide reliable results. How can you make a better prediction? How many people do you need to survey to be 99% confident with a margin of error of 2 percentage points?

What will be an ideal response?

(i) In order to make a better prediction, you want to decrease your poll’s margin of error. To do this, you would simply increase the sample size for the poll. (ii) 4148 people. To determine this, we would substitute the equation of the standard error into the margin of error, so that:
Margin of Error = 2.576(s /n). You would then calculate:
Step 1: 0.02 = 2.576(s /n);
Step 2: 0.02n= n 2.576(s /n);
Step 3: 0.02n = 2.576s;
Step 4: 0.02n/0.02= 2.576s/0.02;
Step 5: n= 128.8s
Following the calculation, you would use the maximum possible standard deviation for a dichotomous variable: s=0.50. So:
Step 1: n= 128.8s
Step 2: n= 128.8(0.50)
Step 3: n= 64.4
Step 4: n= 64.42
Step 5: n= 4147.36