Confidence intervals for means

Specialist Mathematics · Unit 4 — Further calculus and statistical inference · Statistical inference

Learning objectives (7)

LO-1Model and solve problems that involve interval estimates for sample means, with and without technology.LO-2Understand and use the approximate confidence interval (𝑥̅ − 𝑧 𝑠 √𝑛, 𝑥̅ + 𝑧 𝑠 √𝑛), as an interval estimate for 𝜇, the population mean, where 𝑧 is the appropriate quantile for the standard normal distribution.LO-3Understand and use the approximate margin of error. 𝐸 = 𝑧 𝑠 √𝑛 LO-4Understand and use the concept that there are variations in confidence intervals between samples and that most but not all confidence intervals contain 𝜇.LO-5Understand and use the relationship between margin of error, level of confidence and sample size.LO-6Understand the concept of an interval estimate for a parameter associated with a random variable.LO-7Use 𝑥̅ and 𝑠 to estimate 𝜇 and 𝜎, to obtain approximate intervals covering desired proportions of values of a normal random variable and compare with an approximate confidence interval for 𝜇.

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