A-Level Maths Edexcel 9MA0

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.

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.

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.