A-Level Maths OCR A H240

Understand and be able to use 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.

Hypotheses should be stated in terms of parameter values (where relevant) and the meanings of symbols should be stated. For example,

• “$H_0: p=0.7$, $H_1: p \neq 0.7$, where $p$ is the population proportion in favour of the resolution”.

Conclusions should be stated in such a way as to reflect the fact that they are not certain. For example,

• “There is evidence at the $5\%$ level to reject $H_0$. It is likely that the mean mass is less than $500 g$.”
• “There is no evidence at the $2\%$ level to reject $H_0$. There is no reason to suppose that the mean journey time has changed.”

Some examples of incorrect conclusion are as follows:

• “$H_0$ is rejected. Waiting times have increased.”
• “Accept $H_0$. Plants in this area have the same height as plants in other areas.”

Be able to 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 and appreciate that the significance level is the probability of incorrectly rejecting the null hypothesis.

Learners should be able to use a calculator to find critical values.

Includes understanding that, where the significance level of a test is specified, the probability of the test statistic being in the rejection region will always be less than or equal to this level.

The use of normal approximation is excluded.

Recognise that a sample mean, $\bar{X}$, can be regarded as a random variable.

Learners should know and be able to use the result that if $X ∼ N(\mu, \sigma^2)$ then $\bar{X} ∼ N\Bigg(\mu, \dfrac{\sigma^2}{n}\Bigg)$.

The proof is excluded.

Be able to conduct a statistical hypothesis test for the mean of a normal distribution with known, given or assumed variance and interpret the results in context.

Learners should be able to use a calculator to find critical values, but standard tables of the percentage points will be provided in the assessment.

Test for the mean of a non-normal distribution is excluded.

Estimation of population parameters from a sample is excluded.

Understand Pearson’s product-moment correlation coefficient as a measure of how close data points lie to a straight line.

Use and be able to interpret Pearson’s product-moment correlation coefficient in hypothesis tests, using either a given critical value or a $p$-value and a table of critical values.

When using Pearson’s coefficient in an hypothesis test, the data may be assumed to come from a bivariate normal distribution.

A table of critical values of Pearson’s coefficient will be provided.

Calculation of correlation coefficients is excluded.