Lesson 1

Suppose we need to estimate an unknown proportion \(p\) of objects possessing a certain property among all objects (called the population). For example, we may want to find the proportion of people planning to vote for a particular candidate or the proportion of people who own a car. To do this, we repeat the following experiment \(n\) times: we take a random object and check whether it has the desired property. (For simplicity, we assume that each time we return the object, so the probability of selecting an object with the property remains \(p\). In reality, even without replacement, the probability remains almost the same.) Let \(\alpha\) be the number of such objects. Then our statistical estimate of the unknown proportion \(p\) is \(\frac{\alpha}{n}\). Intuitively, the higher \(n\), the closer our estimate is to the true value \(p\). And this is indeed the case.