Hypothesis Testing Basics
Null vs alternative hypotheses.
Key idea
Null vs alternative hypotheses.
In depth
State a null hypothesis H₀ (no effect) and an alternative H₁. Compute a test statistic, find how surprising it is if H₀ were true, and decide. Failing to reject is not proof of H₀.
Worked example
H₀: coin is fair. Getting 9 heads in 10 flips would be rare under H₀.
Real-world uses
- Deciding whether a new teaching method really improved results or just chance
Common mistake
Treating a non-significant result as evidence for H₀.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Hypothesis Testing Basics?
Null vs alternative hypotheses. It is a topic at the expert level in Probability & Statistics.
Where is Hypothesis Testing Basics used in real life?
Real-world examples: Deciding whether a new teaching method really improved results or just chance.
What should I learn before Hypothesis Testing Basics?
Make sure you are comfortable with Confidence Intervals: Proportions, the previous topic in Probability & Statistics.
What is a common mistake with Hypothesis Testing Basics?
Treating a non-significant result as evidence for H₀.
How can I practise Hypothesis Testing Basics?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Hypothesis Testing Basics?
Move on to p-Values next.
Related expert topics in Probability & Statistics
- Skewness and Kurtosis – Measures of asymmetry and tail heaviness.
- Residuals and R² – Error of a fit and proportion of variance explained.
- Simpson’s Paradox – A trend reverses when groups are combined.
- Law of Total Probability – Split an event over a partition.
- Bayes’ Theorem – Update beliefs with evidence.
- Medical Tests and Base Rates – Why positive results can still be probably false.