P-Values and Statistical Significance
A free Statistics and Data Analysis lesson from the “Inference and Conclusions” unit, with a worked example and practice problems including step-by-step solutions.
A p-value measures how unusual the sample result would be if the null hypothesis were true. Statistical significance happens when the p-value is small enough under the chosen significance level. This lesson builds the habit of reading the context first, choosing the right statistical tool, calculating carefully, and then writing what the result means. By the end, students should be able to do the computation and explain why that computation answers the question.
What you'll learn
- Interpret a p-value
- Use a significance level
- Avoid saying the p-value is the probability the null is true
Worked example
Problem. A test has p-value 0.04 and alpha = 0.05. Is the result statistically significant?
- A result is significant when p-value < alpha.
- Here 0.04 < 0.05.
Answer: yes, because 0.04 is less than 0.05
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Practice case A: What does a p-value describe?
Choices: the probability the alternative is true · the sample mean itself · the confidence level · how unusual the data would be if the null were true
Show solution
- The p-value is calculated under the null hypothesis.
- Small values mean the result is unusual under that assumption.
Answer: how unusual the data would be if the null were true
2. Practice case B: At alpha = 0.01, p-value = 0.006 is:
Choices: statistically significant · not statistically significant · proof of the null · a margin of error
Show solution
- A result is significant when p-value is below alpha.
- Each listed p-value is below alpha.
Answer: statistically significant
3. Practice case C: At alpha = 0.05, p-value = 0.07 is:
Choices: a sample proportion · not statistically significant · statistically significant · proof of the alternative
Show solution
- A result is not significant when p-value is above alpha.
- The evidence is not strong enough at that level.
Answer: not statistically significant
4. Practice case D: Which p-value is more surprising under the null?
Choices: 0.65 · 0.90 · 0.01 · 0.20
Show solution
- Smaller p-values are more surprising under the null.
- That means stronger evidence against it.
Answer: 0.01
5. A large study finds a statistically significant difference of 0.01 point on a 100-point test. Which further judgment is still needed?
Choices: Whether the effect is practically important · Whether significance proves a large effect · Whether the null hypothesis has probability exactly zero · Whether the result applies to every population
Show solution
- Statistical significance describes evidence under a null model.
- The effect's size and consequences determine practical importance.
Answer: Whether the effect is practically important
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