Statisticians use hypothesis testing to formally check whether the hypothesis is accepted or rejected. Hypothesis testing is an Inferential Statistical technique used to determine whether there is enough evidence in a data sample to infer that a certain condition holds true for an entire population.

To under the characteristics of a general population, we take a random sample and analyze the properties of the sample. We test whether or not the identified conclusion represents the population accurately and finally we interpret their results. Whether or not to accept the hypothesis depends upon the percentage value that we get from the hypothesis.

To better understand this, let's look at an example.

Consider four boys, Nick, John, Bob and Harry who were caught bunking a class. They were asked to stay back at school and clean their classroom as a punishment.

So, John decided that the four of them would take turns to clean their classroom. He came up with a plan of writing each of their names on chits and putting them in a bowl. Every day they had to pick up a name from the bowl and that person must clean the class.

Now it has been three days and everybody's name has come up, except John's! Assuming that this event is completely random and free of bias, what is the probability of John not cheating?

Let's begin by calculating the probability of John not being picked for a day:

P(John not picked for a day) = 3/4 = 75%

The probability here is 75%, which is fairly high. Now, if John is not picked for three days in a row, the probability drops down to 42%

P(John not picked for 3 days) = 3/4 ×3/4× 3/4 = 0.42 (approx)

Now, let's consider a situation where John is not picked for 12 days in a row! The probability drops down to 3.2%. Thus, the probability of John cheating becomes fairly high.

P(John not picked for 12 days) = (3/4) ^12 = 0.032 <?.??

In order for statisticians to come to a conclusion, they define what is known as a threshold value. Considering the above situation, if the threshold value is set to 5%, it would indicate that, if the probability lies below 5%, then John is cheating his way out of detention. But if the probability is above the threshold value, then John is just lucky, and his name isn't getting picked.

The probability and hypothesis testing give rise to two important concepts, namely:

• Null Hypothesis: Result is no different from assumption.
• Alternate Hypothesis: Result disproves the assumption.

Therefore, in our example, if the probability of an event occurring is less than 5%, then it is a biased event, hence it approves the alternate hypothesis.