A Level statistics

Hypothesis testing is about unusual evidence, not automatic proof.

This prototype uses the normal distribution to show rejection regions, test statistics, p-values and significance levels.

The aim is to help learners connect the diagram, calculation and final conclusion, rather than treating hypothesis tests as a checklist.

Hypothesis testing lab

See rejection regions on the normal distribution

Set up a test for a population mean using a normal model. The shaded area shows the rejection region and the vertical orange line shows the observed test statistic.

z statistic

Critical value

± 1.645

p-value

0.023

Standard error

1.6

Controls

Hypothesised mean: 50

Sample mean: 53.2

Population standard deviation: 8

Sample size: 25

Test type

Significance level

H0: mean = 50

H1: mean is greater than the hypothesised mean.

Reject H0: the observed sample mean is in the rejection region.

What this shows

A hypothesis test asks whether the sample result would be unusual if the null hypothesis were true.

The significance level controls how extreme the result must be before H0 is rejected.

Failing to reject H0 is not the same as proving H0 is true; it means the evidence is not strong enough in this test.

Guided tasks

Move the sample mean slowly. Where does the decision change?

Increase the sample size. Why does the same difference become more significant?

Compare a one-tailed and two-tailed test at the same significance level.

Joy in the process

The point is not just to finish. It is to notice, test and return.

These tools are invitations to explore. A good mistake, a surprising pattern or a question you cannot yet answer is part of the work, not a failure of it.

The challenge is deliberate: the site should support thinking, not remove the need for it.

Before changing a setting, pause and predict what you think will happen.

Change one thing at a time. What stayed the same, and what changed?

Try to create a surprising case, a broken case, or a beautiful pattern.

Ask what this connects to outside the page: maps, movement, nature, systems or decisions.

Reset, then try again with a new question in mind.

Future extensions

This can grow into a broader A Level statistics testing lab.

Add normal probability shading without the hypothesis test context.

Add Type I and Type II error visualisations.

Add binomial hypothesis testing and normal approximation comparisons.

Add exam-style prompts for interpreting conclusions in context.