A complete conclusion links the p-value to the decision, states the decision, and answers the original question in context.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Never say proved
Statistics gives evidence, never proof. "There is convincing evidence that" is the phrasing that earns the mark.
Never accept the null
A large p-value means failing to reject, not accepting. Absence of evidence is not evidence of absence.
Context every time
Name the variable, the population and the direction. A conclusion with no nouns from the problem earns nothing.
Scope of inference
Random sampling permits generalising to the population; random assignment permits a causal claim. Both together permit both.
Interpreting an interval
State the level, the parameter and the population: "We are 95% confident the true mean commute for this town lies between..."
Every conclusion needs context
Name the variable, the population, and the units. A conclusion stated in symbols alone earns little, however correct the arithmetic. The exam is explicitly grading communication.
The right degree of certainty
"We have convincing evidence that..." is appropriate; "we have proved that..." is not. Statistics establishes plausibility, not proof, and answers overstating that are marked down.
State the scope of inference
Random sampling licenses generalisation; random assignment licenses causation. Say which applies and therefore what the conclusion covers. Claiming causation from an observational study is the standard overreach.
A four-part structure
State the procedure, check the conditions, do the mechanics, and state the conclusion in context. Following that structure explicitly is what full-credit answers look like, on every inference question.
Step 2: Try It Yourself
Tap and try it out.
Group 1
Group 2
Group 1 has the most. It has 8 more than Group 2.
Step 3: Watch an Example
One step at a time.
Watch Kofi Write a Conclusion
Kofi has a p-value of 0.02 at alpha 0.05, testing whether a new fertiliser raises yield.
- Step 1
He links the p-value to the threshold: 0.02 is below 0.05.
Step 4: Your Turn
Practice makes it stick.
The Decision
Problem 1 of 2
p-value 0.02 at alpha 0.05. Reject the null? 1 yes, 0 no.
The Wording
Problem 2 of 2
A large p-value. Do you accept the null? 1 yes, 0 no.
Write It Properly
1 of 8
p-value 0.30 at alpha 0.05. Reject the null? 1 yes, 0 no.
2 of 8
Does a statistical test ever prove a claim? 1 yes, 0 no.
3 of 8
What permits generalising to a population? 1 random sampling, 2 random assignment.
4 of 8
What permits a causal claim? 1 random sampling, 2 random assignment.
5 of 8
p-value 0.001 at alpha 0.05. Reject? 1 yes, 0 no.
6 of 8
How many parts does a complete conclusion have: link, decision, context?
7 of 8
Which phrases belong in a correct conclusion?
8 of 8
p-value 0.049 at alpha 0.05. Reject? 1 yes, 0 no.
Step 5: Quick Check
Show what you know.
Question 1 of 2
p-value 0.12 at alpha 0.05. Reject the null? 1 yes, 0 no.
Question 2 of 2
Why is "we accept the null" wrong?
What You Learned
- Link the p-value to the threshold, state the decision, and answer in context.
- Say evidence, never proof, and fail to reject rather than accept.
- Random sampling permits generalisation; random assignment permits causation.