A-Level Maths Specification

OCR A H240

Section 2.05: Statistical hypothesis testing

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#2.05a

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.”

Terms and definitions

#2.05b

Be able to conduct a statistical hypothesis test for the proportion in the binomial distribution and interpret the results in context.

Statistical test using the binomial distribution

#2.05c

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.]

Statistical test using the binomial distribution

#2.05d

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 \(X ∼ N\Bigg(\mu, \dfrac{\sigma^2}{n}\Bigg)\).

[The proof is excluded.]

Statistical test using the Normal distribution

#2.05e

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.]

Statistical test using the Normal distribution

#2.05f

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

Statistical test using correlation coefficients

#2.05g

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.]

Statistical test using correlation coefficients