Hypothesis Testing Basics
So far, we have focused on estimating population values using samples. In many situations, however, we want to make a decision based on data.
Hypothesis testing provides a structured way to use sample data to evaluate claims about a population.
What Is a Hypothesis?
A hypothesis is a statement or claim about a population parameter.
In statistics, hypotheses are tested using sample data to determine whether there is enough evidence to support the claim.
Types of Hypotheses
In hypothesis testing, we always define two competing hypotheses:
- Null Hypothesis (H₀)
- Alternative Hypothesis (H₁ or Hₐ)
Null Hypothesis (H₀)
The null hypothesis represents the default or status-quo assumption.
It usually states that there is no effect, no difference, or no change.
Example:
H₀: The average delivery time is 5 days.
Alternative Hypothesis (H₁)
The alternative hypothesis represents what we are trying to find evidence for.
It suggests that there is an effect, a difference, or a change.
Example:
H₁: The average delivery time is not 5 days.
Why Hypothesis Testing Is Needed
- Helps make data-driven decisions
- Reduces subjective judgment
- Provides a formal testing framework
- Used in science, business, and research
Basic Steps in Hypothesis Testing
| Step | Description |
|---|---|
| 1 | State the null and alternative hypotheses |
| 2 | Choose a significance level |
| 3 | Collect sample data |
| 4 | Calculate a test statistic |
| 5 | Make a decision |
Significance Level (α)
The significance level, denoted by α, represents the probability of rejecting the null hypothesis when it is true.
Common values are:
- 0.05 (5%)
- 0.01 (1%)
A smaller α means stricter evidence is required.
Real-World Example
A company claims its average product weight is 500 grams.
To verify this claim:
- H₀: Mean weight = 500 grams
- H₁: Mean weight ≠ 500 grams
Sample data is collected and tested to decide whether the claim is reasonable.
Decision Outcomes
After testing, we either:
- Reject the null hypothesis
- Fail to reject the null hypothesis
Failing to reject does not mean the null hypothesis is proven true. It only means there is not enough evidence against it.
Common Misunderstandings
- Rejecting H₀ does not prove H₁ is absolutely true
- Failing to reject H₀ does not prove H₀ is true
- Statistical significance is not the same as practical importance
Quick Check
What does the null hypothesis usually represent?
Practice Quiz
Question 1:
Which hypothesis represents the claim being tested?
Question 2:
What does a significance level of 0.05 mean?
Question 3:
Does “fail to reject” mean the null hypothesis is true?
Mini Practice
A restaurant claims its average delivery time is under 30 minutes.
- Form the null hypothesis
- Form the alternative hypothesis
What’s Next
In the next lesson, we will study Type I and Type II Errors, which explain the risks involved in hypothesis testing decisions.