DEFINITION: Hypothesis Testing
A hypothesis test is a statistical test that is used to determine whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population. It examines two opposing hypotheses about a population: the null hypothesis (denoted by \(\text{H}_0\)) and the alternative hypothesis (denoted by \(\text{H}_\text{a}\)).
For example, suppose you suspect that Coke litro contains less than one liter of softdrinks. A null hypothesis might be that the population mean of all Coke litro is one liter. The alternative hypothesis is that the population mean of all Coke litro is less than one liter. Mathematically speaking, the two hypotheses can be expressed using the following:
\[ \text{H}_0: \mu = 1 \text{ liter} \] \[ \text{H}_\text{a}: \mu < 1 \text{ liter} \]
To test the hypothesis, you may get samples of Coke litro (by buying 30 Coke litro) then measure and tally the volume of each Coke. After, you can calculate the test statistic and perform the appropriate statistical tool. From the result, we may conclude to either reject \(\text{H}_0\) and accept \(\text{H}_\text{a}\); or failed to reject \(\text{H}_0\) based on the empirical evidence.
REMARKS: What’s the deal with “failed to reject \(\text{H}_0\)”?
Failing to reject the null hypothesis DOES NOT MEAN that we accept the null hypothesis. It implies that we do not have sufficient evidence, based on our data, to prefer the alternative hypothesis. To explain this further, imagine you are in a trial court. Telling that the suspect is NOT GUILTY (failed to reject the null hypothesis) does not mean that he is INNOCENT (accepting the null hypothesis). Apparently, the complainant side did not provide enough evidence to say that the suspect is GUILTY (reject null and accept alternative hypothesis).