Introductory statistics

University 5 questions

What introductory statistics means

You practise reading data, working with chance, and making simple decisions from samples. This matters because it helps you judge results in tests, reports, and research work with care.

What you will practise

Work out probabilities from simple sample spaces and fraction forms.
Recognise the standard normal distribution and its mean and spread.
Interpret p-values against a chosen significance level.
Decide whether to reject or keep a null hypothesis.

Before you start

You should be comfortable with fractions, percentages, and basic algebra. It also helps if you can read tables and follow simple step-by-step calculations.

Not confident yet? Work through Differential calculus first.

Worked example

One question from this skill's own question bank, shown with its full working.

Question

A p-value of 0.03 at a 5 percent significance level means:

Accept the null hypothesis
Reject the null hypothesis
The test is invalid
The sample is too small

Answer: Reject the null hypothesis

Working: Because 0.03 is less than 0.05, the result is significant and we reject the null hypothesis.

Common mistakes to avoid

Mixing up the p-value and the significance level when making a decision.
Forgetting that the standard normal distribution has mean 0 and standard deviation 1.
Counting favourable outcomes wrongly by missing all valid cases in the sample space.
Treating a small p-value as proof of the alternative hypothesis rather than evidence against the null.

Curriculum and exam alignment

Tertiary foundation coursework

This topic usually appears in early university or tertiary foundation statistics before more advanced inference. It supports later coursework and professional entrance tests where you must interpret data, probability, and hypothesis test results.

Curriculum notes are a general guide to where this work normally sits. Always check the syllabus your school or examination body is currently using.