Practice question · Put in order
Order the reasoning that builds the sampling distribution and its standard error.
- Compute the mean of each sample.
- Collect these sample means into their own distribution (the sampling distribution of the mean).
- Draw many random samples of the same size from a population.
- Its width narrows as each sample gets larger, and that width is the standard error.
- As sample size grows, this distribution approaches a normal shape (the Central Limit Theorem).
Hints
- You cannot have a distribution of means until you have computed many sample means.
- The normal-shape result and the shrinking spread are properties of the distribution once it exists.
Show the answer
- Draw many random samples of the same size from a population.
- Compute the mean of each sample.
- Collect these sample means into their own distribution (the sampling distribution of the mean).
- As sample size grows, this distribution approaches a normal shape (the Central Limit Theorem).
- Its width narrows as each sample gets larger, and that width is the standard error.
Why
Repeated samples yield many means, which form the sampling distribution; that distribution becomes normal as n grows (CLT) and its spread (the standard error) shrinks with n. This chain is why sample means are so predictable.
Practise Sampling and Representativeness
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