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5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you use the chi-squared test for goodness of fit and for independence in a contingency table?

The chi-squared statistic, goodness of fit tests for given distributions, contingency tables and tests for independence, degrees of freedom, and Yates' correction for a two by two table.
A focused answer to the AQA A-Level Further Mathematics chi-squared tests content, covering the chi-squared statistic, goodness of fit tests for given distributions, contingency tables and tests for independence, degrees of freedom, and Yates' correction for a two by two table.
11 min answer →

How do you build a confidence interval for a population mean, and what does the confidence level actually mean?

Confidence intervals for a population mean with known variance, the meaning of a confidence level, the effect of sample size and confidence level on width, and using the t distribution when the variance is unknown.
A focused answer to the AQA A-Level Further Mathematics confidence intervals content, covering confidence intervals for a population mean with known variance, the meaning of a confidence level, the effect of sample size and confidence level on width, and the use of the t distribution when the variance is unknown.
10 min answer →

How do you describe a discrete random variable, and how do you find its expectation and variance?

Probability distributions of discrete random variables, the expectation and variance, the effect of linear coding, and expectation and variance of functions of a random variable.
A focused answer to the AQA A-Level Further Mathematics discrete random variables content, covering probability distributions, the expectation and variance, the effect of linear coding, and the expectation and variance of functions of a random variable.
10 min answer →

How do you carry out hypothesis tests on a Poisson mean and on a population mean, and what do Type I and Type II errors mean?

Hypothesis tests for the mean of a Poisson distribution, tests for a population mean using the normal distribution, one-tailed and two-tailed tests, and the meaning of Type I and Type II errors.
A focused answer to the AQA A-Level Further Mathematics hypothesis testing content, covering tests for the mean of a Poisson distribution, tests for a population mean using the normal distribution, one-tailed and two-tailed tests, and the meaning of Type I and Type II errors.
11 min answer →

When is the Poisson distribution the right model, and how do you calculate and combine Poisson probabilities?

The Poisson distribution as a model for random events, its mean and variance, calculating probabilities, the sum of independent Poisson variables, and the Poisson approximation to the binomial.
A focused answer to the AQA A-Level Further Mathematics Poisson distribution content, covering the Poisson distribution as a model for random events, its mean and variance, calculating probabilities, the sum of independent Poisson variables, and the Poisson approximation to the binomial.
10 min answer →