Hypothesis Testing
HYPOTHESIS TESTING – DETAILED EXPLANATION
1. What is Hypothesis Testing?
Hypothesis testing is a statistical decision-making process used to determine whether a claim about a population is true or not, based on sample data.
In real life, we often make assumptions:
“This medicine works.”
“This teaching method improves results.”
“This machine produces items of the same quality.”
Hypothesis testing allows us to check these assumptions scientifically instead of relying on guesses.
2. Why Hypothesis Testing is Needed
We usually cannot study an entire population because it is:
Too large
Too expensive
Too time-consuming
So we take a sample and use hypothesis testing to make conclusions about the population.
3. Formulation of Hypotheses
a) Null Hypothesis (H₀)
The null hypothesis states that:
There is no effect
There is no difference
The current belief is true
It is the hypothesis that we try to disprove.
Example:
H₀: The average salary of employees is ₹30,000.
b) Alternative Hypothesis (H₁)
The alternative hypothesis states that:
There is an effect
There is a difference
The null hypothesis is not true
Example:
H₁: The average salary of employees is not ₹30,000.
4. Types of Hypothesis Tests
i) Two-Tailed Test
Tests for any difference
Used when direction is not specified
Example:
H₁: μ ≠ 30,000
ii) One-Tailed Test
Tests in one direction only:
Right-tailed: μ > 30,000
Left-tailed: μ < 30,000
Used when we expect a specific increase or decrease.
5. Level of Significance (α)
The level of significance is the probability of rejecting a true null hypothesis.
Common values:
α = 0.05 (5%)
α = 0.01 (1%)
This means we accept a small risk of making a wrong decision.
6. Test Statistic
A test statistic is a number calculated from sample data that helps us decide whether to reject H₀.
Common Test Statistics
| Test | When Used |
| Z-test | Large sample size |
| t-test | Small sample size |
| Chi-square test | Categorical data |
| ANOVA / F-test | More than two means |
7. Sampling Distribution
The sampling distribution shows how the test statistic behaves if the null hypothesis is true. This helps us decide whether the observed result is rare or common.
8. p-Value Concept
The p-value measures how likely the sample result is, assuming H₀ is true.
Decision Rule:
p-value ≤ α → Reject H₀
p-value > α → Accept H₀
A small p-value means the result is unlikely under H₀.
9. Critical Value Approach
Instead of p-value, we can compare:
- Test statistic vs critical value
If the test statistic falls in the rejection region, H₀ is rejected.
10. Steps in Hypothesis Testing
State the null and alternative hypotheses
Choose the level of significance (α)
Select the appropriate statistical test
Collect sample data
Calculate the test statistic
Find p-value or critical value
Make a decision
Draw a conclusion in words
11. Errors in Hypothesis Testing
Type I Error
Rejecting a true null hypothesis
Probability = α
Type II Error
Accepting a false null hypothesis
Probability = β
12. Power of a Test
The power of a test is the probability of correctly rejecting a false null hypothesis.
Power = 1 − β
A higher power means a better test.
13. Practical Example
A company claims that its bulbs last 1000 hours.
H₀: μ = 1000
H₁: μ ≠ 1000
α = 0.05
After testing, p-value = 0.02
Since 0.02 < 0.05, we reject H₀.
Conclusion:
There is sufficient evidence that the average bulb life is different from 1000 hours.
14. Importance of Hypothesis Testing
Supports scientific research
Helps in business decision-making
Used in medicine for drug testing
Ensures quality control in industries
15. Final Summary (Human-Style)
Hypothesis testing is a logical and systematic method that helps us make decisions using data. Instead of trusting assumptions, it allows us to test ideas, reduce uncertainty, and reach reliable conclusions.
