confint - Confidence intervals Suppose we have a set of n...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Confidence intervals Suppose we have a set of n measurements and our model for them is that they are inde- pendent and distributed like X where E ( X ) = μ and SD( X ) = σ . Here μ and σ describe the “state of the world” (as relevant to our experiment) but are not known. In addition, while we don’t know what is causing the variation in measurements, we don’t believe any important factor is changing between measurements so μ and σ 2 remain constant during the sampling and measurement process. Confidence intervals for μ Given some data we want to determine a range of possible μ values that are “reasonable” in a sense we will now consider. We bring together some of the things we saw earlier in the course: (i) we know from the Central Limit Theorem that the sample mean random variable X is approximately N ( μ, σ 2 /n ) (ii) for any number α between 0 and 1 we can use standard Normal tables to find the value z α > 0 such that Φ( z α )- Φ(- z α ) = 1- α ; (iii) hence P- z α < X- μ σ/ √ n < z α = 1- α or P X- μ σ/ √ n > z α = P X- μ > z α σ √ n = α In words this means whatever the true value of μ is, the chance that we observe a sample mean...
View Full Document

This note was uploaded on 05/12/2010 for the course APPLIED ST 2010 taught by Professor Various during the Spring '10 term at Universidad Nacional Agraria La Molina.

Page1 / 2

confint - Confidence intervals Suppose we have a set of n...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online