handout_7_1

# Handout_7_1 - 7.1 Inference for the Mean of a Population the sampling distribution of x depends on when is unknown we must estimate even though we

This preview shows pages 1–3. Sign up to view the full content.

7.1 Inference for the Mean of a Population the sampling distribution of x depends on σ when σ is unknown, we must estimate σ even though we are primarily interested in μ the sample standard deviation ( s ) is used to estimate the population standard deviation (σ) x has N(μ, n σ ) distribution when population has N(μ, σ ) when σ is unknown, we estimate it with the sample standard deviation ( s ) we estimate the standard deviation of x by n s Standard error When the estimated standard deviation is estimated from the data, the result is called the standard error of the statistic. The standard error of the sample mean is x SE = n s one-sample z statistic (6.2) = z = - n x μ ) ( 0 basis for inference about μ when σ is known x distributed normally (or approximately normally)- used Table A when we substitute n s for n , our statistic is not distributed normally the statistic now has a t distribution The t distributions Suppose that an SRS of size n is drawn from a N(μ, σ) population. Then the one-sample t statistic t = - n s x ) ( 0 has the t distribution with n -1 degrees of freedom .

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

View Full Document
t statistic t = - n s x ) ( 0 μ has the t distribution with n -1 degrees of freedom . •there is a different t distribution for each sample size (Table D) •a particular t distribution is specified by giving the degrees of freedom •we use t ( k ) to stand for the t distribution with k degrees of freedom •The density curves of the t ( k ) distributions are similar in shape to the standard normal curve (unimodal, symmetric about 0, and bell-shaped). •As the degrees of freedom
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 02/23/2011 for the course STAT 2700 taught by Professor Bill during the Spring '11 term at Adelphi.

### Page1 / 9

Handout_7_1 - 7.1 Inference for the Mean of a Population the sampling distribution of x depends on when is unknown we must estimate even though we

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online