Specification Ref. Learning outcomes Notes Notation Exclusions STATISTICS: STATISTICAL HYPOTHESIS TESTING (1) Hypothesis testing for a binomial probability p H4 Be able to identify null and alternative hypotheses (H0 and H1) when setting up a hypothesis test based on a binomial probability model. H0 of form p = a particular value, with p a probability for the whole population. H0, H1 H5 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. Normal approximation. H6 Be able to identify the critical and acceptance regions. STATISTICS: STATISTICAL HYPOTHESIS TESTING (2) Hypothesis testing for a mean using Normal distribution MH7 Know that random samples of size n from have the sample mean Normally distributed with mean and variance . Sample mean, Particular value of sample mean, Population mean, Central Limit Theorem H8 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 pvalue or a critical region. H0 of form µ = a particular value, where µ is the population mean. Significance level will be given. H9 Be able to identify the critical and acceptance regions.
Conceptual links to other areas of the specification There is a lot of problem solving involved in statistical hypothesis testing; learners need to be able to extract the information they need from the questions and data given in order to arrive at a solution. Learners must have a clear understanding of the basics of probability distributions and how they can be applied to perform statistical hypothesis testing. Teachers should ensure that time is spent on longer questions so that learners have the opportunity to extract the data they need and ignore extraneous information. It is strongly suggested that teachers provide as many real life uses of statistical hypothesis testing from other topic areas and different real world examples to emphasise the relevance of this area of mathematics to learners.
Resources Title Organisation Description Ref MEI A commentary of the underlying mathematics, a sample resource, a use of technology, links with other topics, common errors and questions to promote mathematical thinking. H1, H2, H3, H4, H5 and H6 CAUSE A simple story and a worksheet with questions to guide the students. The teaching material is intended to be flexible depending on the time available. Instructors can choose to do just the interactive lecture type, interactive lecture + activity, or even add the optional material. H1, H2, H3, H4, H5 and H6 Wiley A full set of class teacher’s notes and lesson plans on hypothesis testing that can be adapted. All solutions to the examples are given. This goes on to confidence levels. H1, H2, H3, H4, H5 and H6 Exam Solutions In this video, hypothesis testing for the binomial distribution is introduced along with notation used, one-tail tests and significance levels. The conditions that are needed to consider in order to accept or reject the null hypothesis are also covered. H4, H5, H6 MathsAcademyUK3 Video demonstration of Hypothesis Testing - The Population Proportion p, using a Binomial Distribution - 2 tailed test. Goes into splitting the Significance Level. And using the Critical Values Method. H4, H5, H6 Geogebra Interactive resource representing Hypothesis test using the binomial distribution. H4, H5 and H6
Geogebra Interactive demonstration. H7, H8 and H9 CPALMS A full lesson plan on using the correlation coefficient. Worked examples and assessments are included. H10 and H11 ProfNoria A video using an example to show how to use Pearson’s product moment correlation coefficient for hypothesis testing. H10 and H11 r statslectures A video with a situation and full worked example including calculations for Pearson’s product moment correlation coefficient. H10 and H11