Understand and apply the language of statistical hypothesis testing, developed through a binomial model: null hypothesis, alternative hypothesis, significance level, test statistic, 1-tail test, 2-tail test, critical value, critical region, acceptance region, \(p\)-value.

An informal appreciation that the expected value of a binomial distribution is given by \(np\) may be required for a 2-tail test.

Extend to correlation coefficients as measures of how close data points lie to a straight line.

Students should know that the product moment correlation coefficient \(r\) satisfies \(|r| ≤ 1\) and that a value of \(r = ±1\) means the data points all lie on a straight line.

Be able to interpret a given correlation coefficient using a given \(p\)-value or critical value (calculation of correlation coefficients is excluded).

Students will be expected to calculate a value of r using their calculator but use of the formula is not required.

Hypotheses should be stated in terms of \(p\) with a null hypothesis of \(p = 0\) where \(p\) represents the population correlation coefficient.

Tables of critical values or a \(p\)-value will be given.

Terms and definitions Statistical test using correlation coefficients

Conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret the results in context.

Understand that a sample is being used to make an inference about the population.

Hypotheses should be expressed in terms of the population parameter \(p\).

Appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis.

A formal understanding of Type I errors is not expected.

Statistical test using the binomial distribution

Conduct a statistical hypothesis test for the mean of a Normal distribution with known, given or assumed variance and interpret the results in context.

Students should know that:

If \(X∼N(μ, σ^2)\) then \(\bar{X}∼N\Bigg(μ,\dfrac{σ^2}{n}\Bigg)\)

and that a test for \(μ\) can be carried out using:

\(\dfrac{\bar{X}-μ}{σ/\sqrt{n}}∼N(0,1^2)\).

No proofs required.

Hypotheses should be stated in terms of the population mean \(μ\).

Knowledge of the Central Limit Theorem or other large sample approximations is not required.

Statistical test using the Normal distribution