Understand the process of hypothesis testing and the associated language.

Null hypothesis, alternative hypothesis. Significance level, test statistic, 1-tail test, 2-tail test.
Critical value, critical region (rejection region), acceptance region, \(p\)-value.

Terms and definitions

Understand when to apply 1-tail and 2-tail tests.

Terms and definitions

Understand that a sample is being used to make an inference about the population and appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis.

For a binomial hypothesis test, the probability of the test statistic being in the rejection region will always be less than or equal to the intended significance level of the test, and will usually be less than the significance level of the test. Learners will not be tested on this distinction. If asked to give the probability of incorrectly rejecting the null hypothesis for a particular binomial test, either the intended significance level or the probability of the test statistic being in the rejection region will be acceptable.

Terms and definitions

Be able to identify null and alternative hypotheses (\(H_0\) and \(H_1\)) when setting up a hypothesis test based on a binomial probability model.

\(H_0\) of form \(p =\) a particular value, with \(p\) a probability for the whole population.

Notation: \(H_0\), \(H_1\)

Statistical test using the binomial distribution

Be able to conduct a hypothesis test at a given level of significance. Be able to draw a correct conclusion from the results of a hypothesis test based on a binomial probability model and interpret the results in context.

[Excludes: Normal approximation]

Statistical test using the binomial distribution

Be able to identify the critical and acceptance regions.

Statistical test using the binomial distribution

Know that random samples of size \(n\) from \(X ∼ N(\mu, \sigma^2)\) have the sample mean Normally distributed with mean \(\mu\) and variance \(\dfrac{\sigma^2}{n}\).

Notation:
Sample mean, \(\bar{X}\)
Particular value of sample mean, \(\bar{x}\)
Population mean, \(\mu\)

[Excludes: Central Limit Theorem]

Statistical test using the Normal distribution

Be able to carry out a hypothesis test for a single mean using the Normal distribution and be able to interpret the results in context.

In situations where either
(a) the population variance is known or
(b) the population variance is unknown but the sample size is large
Learners may be asked to use a \(p\)‑value or a critical region.
\(H_0\) of form \(\mu =\) a particular value, where \(\mu\) is the population mean.
Significance level will be given.

Statistical test using the Normal distribution

Be able to identify the critical and acceptance regions.

Statistical test using the Normal distribution

Understand correlation as a measure of how close data points lie to a straight line.
Understand that a rank correlation coefficient measures the correlation between the data ranks rather than actual data values.

Learners are not required to know the names of particular correlation coefficients.

Notation: \(r\)

[Excludes: Calculation of correlation coefficient]

Statistical test using correlation coefficients

Be able to use a given correlation coefficient for a sample to make an inference about correlation or association in the population for given \(p\)-value or critical value.

Association refers to a more general relationship between the variables.
The (often implicit) null hypothesis is of the form either that there is no correlation or no association in the population. Questions will use an appropriate correlation coefficient and indicate whether correlation or association is being tested for.

Questions may require understanding of notation from software; sufficient guidance will be given in the question.

[Excludes: Knowledge of bivariate Normal distribution]

Statistical test using correlation coefficients