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Topic 6: Sampling and Confidence Intervals

3 dot points, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

How do we use one sample to estimate a plausible range for the population mean?

A confidence interval gives a range of plausible values for the population mean, built from the sample mean plus or minus a critical z-value times the standard error.

How to construct and correctly interpret a confidence interval for a population mean, the critical z-values for common confidence levels, and worked calculations.

8 min read →

How large a sample do we need to achieve a required level of precision?

The margin of error sets the precision of an estimate; rearranging it determines the sample size needed for a target margin.

What the margin of error is, how it depends on confidence level and sample size, and how to rearrange the formula to find the sample size needed for a required precision.

8 min read →

How does the mean of a sample behave when we take many samples from a population?

The sampling distribution of the sample mean is approximately normal, centred on the population mean, with a standard deviation that shrinks as the sample size grows.

What a sampling distribution is, the mean and standard error of the sample mean, and how the Central Limit Theorem makes the sample mean approximately normal.

8 min read →