# 22 Statistics 3

Candidates will be expected to be familiar with the knowledge, skills and understanding implicit in the modules Statistics 1 and 2 and Core 1 and 2.

Candidate may use relevant formulae included in the formulae booklet without proof.

Candidates should learn the following formulae, which are **not** included in the formulae booklet, but which may be required to answer questions.

For independently distributed , then

is distributed

Power = 1 – P(Type error)

Bayes’ Theorem. | Knowledge and application to at most three events.
The construction and use of tree diagrams |

Mean, variance and standard deviation of a linear combination of two (discrete or continuous) random variables. | To include covariance and correlation. Implications of independence. Applications, rather than proofs, will be required. |

Mean, variance and standard deviation of a linear combination of independent (discrete or continuous) random variables. | Use of these, rather than proofs, will be required. |

Linear combinations of independent normal random variables. | Use of these only. |

Mean, variance and standard deviation of binomial and Poisson distributions. | Proofs using and together with . |

A Poisson distribution as an approximation to a binomial distribution. | Conditions for use. |

A normal distribution as an approximation to a binomial distribution. | Conditions for use. Knowledge and use of continuity corrections. |

A normal distribution as an approximation to a Poisson distribution. | Conditions for use. Knowledge and use of continuity corrections. |

Estimation of sample sizes necessary to achieve confidence intervals of a required width with a given level of confidence. | Questions may be set based on a knowledge of confidence intervals from the module Statistics 1. |

Confidence intervals for the difference between the means of two independent normal distributions with known variances. | Symmetric intervals only. Using a normal distribution. |

Confidence intervals for the difference between the means of two independent distributions using normal approximations. | Large samples only. Known and unknown variances. |

The mean, variance and standard deviation of a sample proportion. | |

Unbiased estimator of a population proportion. | |

A normal distribution as an approximation to the sampling distribution of a sample proportion based on a large sample. | |

Approximate confidence intervals for a population proportion and for the mean of a Poisson distribution. | Using normal approximations. The use of a continuity correction will not be required in these cases. |

Approximate confidence intervals for the difference between two population proportions and for the difference between the means of two Poisson distributions. | Using normal approximations. The use of continuity corrections will not be required in these cases. |

The notion of the power of a test. | Candidates may be asked to calculate the probability of a Type error or the power for a simple alternative hypothesis of a specific test, but they will not be asked to derive a power function. Questions may be set which require the calculation of a -statistic using knowledge from the module Statistics 1. The significance level to be used in a hypothesis test will usually be given. |

Tests for the difference between the means of two independent normal distributions with known variances. | Using a -statistic. |

Tests for the difference between the means of two independent distributions using normal approximations. | Large samples only. Known and unknown variances. |

Tests for a population proportion and for the mean of a Poisson distribution. | Using exact probabilities or, when appropriate, normal approximations where a continuity correction will not be required. |

Tests for the difference between two population proportions and for the difference between the means of two Poisson distributions. | Using normal approximations where continuity corrections will not be required. In cases where the null hypothesis is testing an equality, a pooling of variances will be expected. |

Use of the supplied tables to test for a bivariate normal population. | Where denotes the population product moment correlation coefficient. |

## Specification

The **last January exams** for AS and A2 were in **January 2013**.

The exams are now **only in June** due to Changes to A-levels.

- Specification for exams from 2014 (3.1 MB)