P&SIA L1 C4 S3

Intro Stats Islamic Approach -- Part 2 Prob & Stats

Lecture 1 Random Samples, Concept 4: Simple Random Samples

S3: Examples of Representation

One of the most important ways in which Statistics is used is by drawing random samples to study large populations. Some examples of this process and how it is used are given below.

Example 1: Pre-Election Polls

We want to find out who is going to win the upcoming elections. Draw a simple random sample SRS of 1000 Voters V1, V2, ... V(1000) chosen at random from the entire population of registered Voters in Pakistan. Ask them which party they will vote for -- PML or PPP -- let's keep it down to two for simplicity.

Suppose we find that 350 are planning to vote for PML, 250 are planning to vote for PPP, and 400 are undecided, or not planning to vote at all. According to the Law of Large Numbers, proportions in the sample should resemble proportions in the population. So we would make the iNFERENCE that PML will receive 35% of the vote, PPP will receive 25% of the vote, Voter turnout will be 60% and 40% of registered voters will not cast votes in the election.

Polls are not just useful for predicting results, but are also important guides to action. For example, a poll like the above shows that many people are undecided, and so a party may start a campaign to try to win over these undecided people, so as to win the election. Opinion polls may be taken to find out which issues people care the most about, so that the parties can put together some campaign promises which will appeal to the people. ALL this is possible because of random samples -- these allow us to find out about the public opinion in the whole country of 160 million by asking just 3000 voters.