Surveys of a Population

Say a company wanted to hire musicians for a big concert for a certain city. They might wonder whether sufficient numbers of people would attend to make it financially worthwhile. They could interview everybody in the city who is old enough to attend and ask them if they were going to buy tickets. This would take an enormous amount of time though, and so statisticians usually get data from a portion of the population ( a sample is used) and may use this data to predict the probability of events occurring.

Now if data was collected from a rich area (this type of person is likely to have money to buy tickets) it might be found that a high percentage wants to buy tickets. If the data was collected in a poor area it might be found that a low percentage wants to buy tickets.

The statisticians would like a sample that helps them predict. Hopefully they could get a sample that would tell them fairly accurately what percentage of the city would attend. One way to do this would be to choose a street that all types of people walk along and get a random sample. For instance every 10th passer-by may be asked if he or she is going to buy a ticket. If one had a group of people of all types one could also use a table of random numbers to choose a random sample, and there are other methods.

Once a satisfactory sample had been obtained the statistician could get an idea of what percentage of the population would attend and the probability that this percentage would lie in a certain range (say from 10% to 14%) The larger the sample the more accurately one can usually predict. After calculations the statistician might conclude that he/she is 95% sure that the percentage of people who will buy tickets lies between 11% and 16%

Example: A city councilor wants to know what percentage of the vote he will get in an election. Jake from his office goes out to do a survey. Jake stands outside a supermarket, feeling that he will get a sample here that is representative of the voters. He asks every fifth passer by to tick an appropriate box on a piece of paper and put the paper in a box (so that people can record who they will vote for without letting anyone know who it is).

After this and back at the office Jake uses a computer program to give him a confidence interval (a free program called ConfTwoProp can be downloaded at http://www.4shared.com/dir/6vUP2Vn9/sharing.html to do this should you want to do your own survey).