To understand why we need Hypothesis testing , lets go through a concrete real time example. Let say a beverage company claims that their beverage bottles will always contain atleast 50ml. To test their claim, we cannot take all the available bottles in the world and check them; rather we will take random set of those bottles (called Sample) and find the mean.
Now, the question is, whether the mean that we find using the sample represent the actual mean of the entire population ?
Let say we got 10 bottles randomly from near by stores, and measure the volume of each bottle and calculated average as below.
(50.5 + 49.3 + 50.3+51.2 + 50.6 + 50.9 + 48.2 + 50.5 + 49.6 +51.3 ) / 10 = 50.24ml
Can we conclude that what the company claims is really true ?
We need to ask the above question, because there are chances that the 10 samples that we collected are by chance/luck can possibly favour the companies claim, because different samples will have different mean,
If the actual population mean is as below, then we may change our opinion about the company claim.
Here, the actual mean of the population is 35 , and as we see , there is only 15% of chance that we get atleast 50 ml.
Now we are in situation to understand further to agree/disagree to company claim.
Can we agree if the percentage is 30% or 40% e.t.c ? Such kind of questions raises to the study of Hypothesis Testing which gives tools and steps to test the claim or an experiment.
