Further Pure Maths 1 Further Maths 2 Further Mechanics Further Statistics

Use a Wilcoxon rank-sum test, as appropriate, to test for identity of populations.

Use a Wilcoxon matched-pairs signed-rank test as appropriate, to test for identity of populations.

Use a paired-sample sign test as appropriate, to test for identity of populations.

Use a a single-sample Wilcoxon signed-rank test to test a hypothesis concerning a population median

Use a single-sample sign test to test a hypothesis concerning a population median

Sign Test PPT Paired Sign Test PPT One Sample Wilcoxon Sign Rank Test PPT Wilcoxon-Matched-Pairs Sign-Rank Test PPT Wilcoxon Rank-Sum Test PPT

Sign Test PPT Paired Sign Test PPT One Sample Wilcoxon Sign Rank Test PPT Wilcoxon-Matched-Pairs Sign-Rank Test PPT Wilcoxon Rank-Sum Test PPT

Sign Test PPT Paired Sign Test PPT One Sample Wilcoxon Sign Rank Test PPT Wilcoxon-Matched-Pairs Sign-Rank Test PPT Wilcoxon Rank-Sum Test PPT

Sign Test PPT Paired Sign Test PPT One Sample Wilcoxon Sign Rank Test PPT Wilcoxon-Matched-Pairs Sign-Rank Test PPT Wilcoxon Rank-Sum Test PPT

Formulate hypotheses concerning the difference of population means, and apply, as appropriate – a paired sample t-test – a test using a normal distribution

Calculate a pooled estimate of a population variance from two samples Formulate hypotheses concerning the difference of population means, and apply, as appropriate – a 2-sample t-test – a test using a normal distribution

Formulate hypotheses and apply a hypothesis test concerning the population mean using a small sample drawn from a normal population of unknown variance, using a t-test

Determine a confidence interval for a population mean, based on a small sample from a normal population with unknown variance, using a t-distribution Determine a confidence interval for a difference of population means, using a t-distribution or a normal distribution, as appropriate.

Formulate hypotheses and apply a hypothesis test concerning the population mean using a small sample drawn from a normal population of unknown variance, using a t-test Calculate a pooled estimate of a population variance from two samples Formulate hypotheses concerning the difference of population means, and apply, as appropriate – a 2-sample t-test – a paired sample t-test – a test using a normal distribution Determine a confidence interval for a population mean, based on a small sample from a normal population with unknown variance, using a t-distribution Determine a confidence interval for a difference of population means, using a t-distribution or a normal distribution, as appropriate.

Formulate hypotheses and apply a hypothesis test concerning the population mean using a small sample drawn from a normal population of unknown variance, using a t-test Calculate a pooled estimate of a population variance from two samples Formulate hypotheses concerning the difference of population means, and apply, as appropriate – a 2-sample t-test – a paired sample t-test – a test using a normal distribution Determine a confidence interval for a population mean, based on a small sample from a normal population with unknown variance, using a t-distribution Determine a confidence interval for a difference of population means, using a t-distribution or a normal distribution, as appropriate.

Formulate hypotheses and apply a hypothesis test concerning the population mean using a small sample drawn from a normal population of unknown variance, using a t-test Calculate a pooled estimate of a population variance from two samples Formulate hypotheses concerning the difference of population means, and apply, as appropriate – a 2-sample t-test – a paired sample t-test – a test using a normal distribution Determine a confidence interval for a population mean, based on a small sample from a normal population with unknown variance, using a t-distribution Determine a confidence interval for a difference of population means, using a t-distribution or a normal distribution, as appropriate.

Understand the concept of a probability generating function (PGF) and construct and use the PGF for given distributions e.g discrete uniform, binomial, geometric and Poisson distributions Use formulae for the mean and variance of a discrete random variable in terms of its PGF, and use these formulae to calculate the mean and variance of a given probability distribution Use the result that the PGF of the sum of independent random variables is the product of the PGFs of those random variables.

Understand the concept of a probability generating function (PGF) and construct and use the PGF for given distributions e.g discrete uniform, binomial, geometric and Poisson distributions Use formulae for the mean and variance of a discrete random variable in terms of its PGF, and use these formulae to calculate the mean and variance of a given probability distribution Use the result that the PGF of the sum of independent random variables is the product of the PGFs of those random variables.

Understand the concept of a probability generating function (PGF) and construct and use the PGF for given distributions e.g discrete uniform, binomial, geometric and Poisson distributions Use formulae for the mean and variance of a discrete random variable in terms of its PGF, and use these formulae to calculate the mean and variance of a given probability distribution Use the result that the PGF of the sum of independent random variables is the product of the PGFs of those random variables.