Hypothesis Test , Fact Vs Illusion | OpexEdge Consultancy - Architecting Business Transformation from Zero to Scale.

Hypothesis testing is a statistical method used to decide whether there is enough evidence in a sample to support a claim about a population.

Main idea

You start with two competing statements:

Null hypothesis $H_0)$ : usually says there is no effect, no difference, or no relationship.
Alternative hypothesis $Ha)(H_1 \text{ or } H_a)$ : says there is an effect, difference, or relationship.

Example

Suppose a company claims that the average battery life of its product is 10 hours.

$μ=10H_0:\ \mu = 10$
$μ≠10H_1:\ \mu \neq 10$

You test a sample of batteries. If the results are very unlikely to happen when the average is truly 10 hours, you reject the null hypothesis.

Basic steps

State $H_0$ and $H_1$ .
Choose a significance level, usually:
$α=0.05\alpha = 0.05$
Collect sample data.
Calculate a test statistic and a p-value.
Compare the p-value with $α\alpha$ .

Decision rule:

If p-value $≤α\leq \alpha$ : reject $H_0$ .
If p-value $\alpha$ : fail to reject $H_0$ .

Important wording

You usually say “fail to reject the null hypothesis”, not “accept the null hypothesis,” because the test may not prove that $H_0$ is true. It only shows whether the evidence against it is strong enough.

Types of errors

Error	Meaning
Type I error	Rejecting $H_0$ when it is actually true
Type II error	Failing to reject $H_0$ when it is actually false

Common hypothesis tests

Test	Used for
t-test	Comparing averages
z-test	Testing averages or proportions with large samples
Chi-square test	Testing relationships between categorical variables
ANOVA	Comparing three or more averages
Correlation test	Checking whether two variables are related

In simple words, hypothesis testing helps you decide whether an observed result is likely a real effect or could have happened by random chance.