Introduction to hypothesis testing — Edexcel A-Level Statistics
Test yourself on Introduction to hypothesis testing with PEARSON EDEXCEL A-Level practice questions.
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Introduction to hypothesis testing explained
A parameter is a fixed numerical characteristic of a population, such as the population mean μ or proportion p.
Read the full explanation
A statistic is a numerical characteristic calculated from a sample, such as the sample mean x̄ or sample proportion p̂, used to estimate the parameter. An estimator is unbiased if its sampling distribution has mean equal to the true parameter value; for example, the sample mean is an unbiased estimator of μ because E(x̄) = μ. Standard error is the standard deviation of a statistic's sampling distribution; for the sample mean it is σ/√n, and for a sample proportion it is √(p(1−p)/n). Understanding these terms lets you distinguish population values from sample estimates and quantify the precision of an estimate.
Your focus
- Distinguish between a parameter and a statistic in context.
- Explain what it means for an estimator to be unbiased.
- Calculate and interpret the standard error of a sample mean or proportion.
Introduction to hypothesis testing exam tips
Marking Points
- Defines a parameter as a fixed numerical characteristic of a population, e.g. μ or p.
- Defines a statistic as a numerical characteristic calculated from a sample, e.g. x̄ or p̂.
- Explains that an estimator is unbiased if its expected value equals the true parameter value.
- States that standard error is the standard deviation of the sampling distribution of a statistic.
- Gives the standard error of the sample mean as σ/√n (or s/√n when σ is unknown).
- Gives the standard error of a sample proportion as √(p(1−p)/n) (or √(p̂(1−p̂)/n) when p is unknown).
Examiner Tips
- 💡In multiple-choice questions, check whether the option refers to a population value or a sample value before selecting it.
- 💡When a formula is given, verify the denominator: standard error of the mean uses √n, not n.
- 💡For unbiasedness, look for the condition E(estimator) = parameter; if the expected value differs, the estimator is biased.
Common Mistakes
- Confusing parameter and statistic: a parameter describes the population and is usually unknown, while a statistic describes a sample and is calculated from data.
- Thinking any sample statistic is unbiased: unbiasedness requires the sampling distribution's mean to equal the parameter, which is not automatic.
- Mixing up standard deviation and standard error: standard deviation measures spread of individual observations, while standard error measures spread of a statistic's sampling distribution.
- Using n instead of √n in the standard error formula: the correct denominator for the sample mean is √n, not n.