IB Maths AI 4.11 Definitions

This page contains our IB Maths AI definitions for 4.11. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Confidence intervals'.

All Topic 4 Sub-topics 4.1: Fundamentals Of Statistics 4.2: Visualising Statistics 4.3: Distribution Properties 4.4: Introduction To Linear Statistics 4.5: Probability 4.6: Probability Distributions 4.7: Hypotheses & Tests (HL)4.8: Data collection & categorisation (HL)4.9: Advanced linear statistics (HL)4.10: Linear transformations & combinations (HL)4.11: Confidence intervals (HL)4.12: Poisson distribution (HL)4.13: Distribution tests (HL)4.14: Transition matrices

confidence

A statement about the long-run performance of an interval-building method; for example, with a

95\%

method, about

95\%

of intervals from repeated samples would contain the true population mean.

confidence interval

A range of plausible values for a population mean, built around the sample mean to show uncertainty due to sampling.

degrees of freedom

The number of independent pieces of information used to determine the sampling distribution of a test statistic; for $\chi^2$ independence it is $(\text{rows}-1)(\text{columns}-1)$ and for goodness of fit it is $n-1$ .

margin of error

The half-width of a confidence interval, equal to a critical value multiplied by a standard error, such as

z\frac{\sigma}{\sqrt{n}}

t\frac{s}{\sqrt{n}}

normal

A line through a point on a curve that is perpendicular to the tangent at that point, with gradient equal to the negative reciprocal of the tangent gradient.

sample mean

The arithmetic average of the sample values, given by '

\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i

', and used as an unbiased estimator of '

\mu

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