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LearnEdexcel9FM0First teaching 2017Option · Further Statistics 2Estimation, confidence intervals and tests

Option · Module

Estimation, confidence intervals and tests

3 subtopics≈ 115 min in total

Start the module: Sampling and unbiased estimates Open graphing calculator

Sampling and unbiased estimates
We usually can't measure a whole population, so we measure a random sample and estimate. The sample mean estimates $\mu$ fairly, but for the variance we divide by $n-1$ , not $n$ , to stop the estimate coming out too small on average.
≈ 35 min
Confidence intervals
A single estimate is almost certainly a little wrong. A confidence interval gives a range, $\bar x\pm z\dfrac{\sigma}{\sqrt n}$ , built so that in, say, $95\%$ of samples the range would capture the true mean.
≈ 40 min
Tests for a population mean
Has the average changed? Assume it hasn't, work out how many standard errors the sample mean is from the claimed mean, and compare that $z$ with the critical value for your significance level.
≈ 40 min