Sampling, estimates and resampling — Edexcel A-Level Statistics
Test yourself on Sampling, estimates and resampling with PEARSON EDEXCEL A-Level practice questions.
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Sampling, estimates and resampling explained
A parameter is a numerical characteristic of a population, such as the population mean μ or population proportion p, and is usually unknown.
Read the full explanation
A statistic is a numerical characteristic calculated from a sample, such as the sample mean x̄, and is used to estimate the parameter. An estimator is unbiased if its sampling distribution has mean equal to the true parameter value, so it does not systematically overestimate or underestimate. The standard error is the standard deviation of the sampling distribution of a statistic; for a sample mean from independent observations with population standard deviation σ, it is σ divided by the square root of n. Increasing sample size reduces the standard error, so estimates become more precise. For example, the sample mean is an unbiased estimator of the population mean, and its standard error measures how much sample means vary from sample to sample.
Your focus
- Define and distinguish the terms parameter and statistic in context.
- Explain what it means for an estimator to be unbiased.
- Calculate and interpret the standard error of a sample mean.
Sampling, estimates and resampling exam tips
Marking Points
- A parameter is a numerical characteristic of a population, for example the population mean μ or population proportion p.
- A statistic is a numerical characteristic calculated from sample data, for example the sample mean x̄ or sample proportion.
- An estimator is unbiased when the mean of its sampling distribution equals the true value of the parameter being estimated.
- The standard error is the standard deviation of the sampling distribution of a statistic.
- For the sample mean of independent observations, the standard error is σ divided by the square root of n, where σ is the population standard deviation and n is the sample size.
- The standard error decreases as sample size increases, indicating greater precision of the estimate.
Examiner Tips
- 💡State clearly whether a quantity refers to the population or to a sample before naming it a parameter or a statistic.
- 💡When explaining unbiasedness, refer to the sampling distribution and its mean rather than to one observed estimate.
- 💡Quote the standard error formula for the sample mean as σ divided by the square root of n and identify each symbol.
Common Mistakes
- Treating a parameter and a statistic as interchangeable; correction: a parameter describes the population and is usually unknown, while a statistic is calculated from a sample.
- Saying an unbiased estimator always gives an estimate equal to the parameter; correction: unbiasedness concerns the mean of the sampling distribution over repeated samples, not any single estimate.
- Confusing standard error with standard deviation of the sample; correction: the standard error is the standard deviation of the sampling distribution of the statistic.
- Thinking standard error increases with sample size; correction: for the sample mean it is σ divided by the square root of n, so it decreases as n increases.