Use a t-test to compare two means
Use the supplied t-test formula and critical values to assess whether two sample means differ significantly.
A Level; Cambridge International Biology 9700, 2028–2030. Written answers and calculations are self-checked; this is not fieldwork or practical-skills certification.
Before you begin
- Populations contain inherited variation, and alleles can be transmitted from parents to offspring.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does the t-test compare in this syllabus outcome?
What you will learn
- Use a t-test to compare means of two samples
- Interpret the result relative to a null hypothesis, degrees of freedom and supplied critical value
Original teaching model. Measurements, categories, DNA fragments and comparison records are invented; assumptions and sample boundaries are stated.
| Feature | Meaning |
|---|---|
| Classes | 40–<50 / 50–<60 / 60–<70 / 70–<80 mm |
| Counts | 4 / 7 / 6 / 3; total 20 |
| Percentages | 20% / 35% / 30% / 15% |
| Raw-data mean | 1168 mm ÷ 20 = 58.4 mm |
Build the evolutionary explanation
Use a t-test to assess the significance of a difference between two samples with continuous data, including samples with fewer than 30 observations. The data should come from normally distributed populations with approximately equal standard deviations. Compare their means using the supplied formula, then calculate degrees of freedom v=n1+n2−2. State a null hypothesis that the two population means do not differ significantly. Compare the calculated t with the supplied critical value at the chosen significance level. If calculated t exceeds the critical value, reject the null hypothesis; otherwise there is insufficient evidence to reject it.
Interpret data with care
A significant difference does not prove that the tested factor caused the difference. Check that samples are appropriate, the correct formula and degrees of freedom are used, and the comparison is at the stated significance level. The formula is supplied in the examination.
Pause and explain
You are given two sample means, sample sizes and a critical-value table. Outline the sequence for a t-test.
Worked example
A calculated t is below the critical t value at p=0.05. What is the conclusion?
Show the worked solution
- Compare calculated and critical values.
- A smaller calculated value is not significant at that level.
Answer There is insufficient evidence to reject the null hypothesis at p=0.05; the difference is not significant by this test.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A calculated t exceeds the supplied critical t value. State the statistical conclusion.
Give me a hint
Identify the population-level variable and sequence the mechanism.
Compare my reasoning
- The calculated statistic exceeds the rejection threshold.
- Reject the null hypothesis at the stated significance level.
Reject the null hypothesis: the sample means differ significantly at the stated significance level. This does not by itself identify the cause.
Look for these in your work
- Population process identified
- Cause and consequence linked
A learner says p>0.05 proves that two population means are identical. Correct the claim.
Give me a hint
Use the supplied sample or condition to justify the conclusion.
Compare my reasoning
- A non-significant result is insufficient evidence to reject the null.
- It is not proof of exact equality.
A non-significant result means there is insufficient evidence to reject the null hypothesis at that level; it does not prove the population means are identical.
Look for these in your work
- Evidence interpreted
- Assumptions stated
You are given two sample means, sample sizes and a critical-value table. Outline the sequence for a t-test.
Give me a hint
Apply the population model to the new example and qualify its limits.
Compare my reasoning
- State the null hypothesis and use the supplied formula.
- Find degrees of freedom and compare calculated and critical t.
State the null hypothesis; use the supplied t-test formula; determine the required degrees of freedom; compare calculated t with the critical value at the stated significance level; and state whether there is sufficient evidence to reject the null.
Look for these in your work
- Model applied
- Limits preserved
Common mistakes
- Using a chi-squared test to compare sample means
- Claiming a non-significant result proves the means are equal
What can you explain now?
What does the t-test compare in this syllabus outcome?
Compare with the explanation
Means of two samples
The test evaluates whether the difference between sample means is statistically significant.
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Make it stick
How does the calculated t value determine the conclusion?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.