Chapter_17

Chapter_17 - Chapter 17 Inference about a Population Mean...

This preview shows pages 1–10. Sign up to view the full content.

BPS - 5th Ed. Chapter 17 1 Chapter 17 Inference about a Population Mean

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

View Full Document
BPS - 5th Ed. Chapter 17 2 Conditions for Inference about a Mean Data are from a SRS of size n . Population has a Normal distribution with mean μ and standard deviation σ . Both and are usually unknown. we use inference to estimate . Problem: unknown means we cannot use the z procedures previously learned.
BPS - 5th Ed. Chapter 17 3 When we do not know the population standard deviation σ (which is usually the case), we must estimate it with the sample standard deviation s . When the standard deviation of a statistic is estimated from data, the result is called the standard error of the statistic. The standard error of the sample mean is Standard Error x s n

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

View Full Document
BPS - 5th Ed. Chapter 17 4 When we estimate σ with s , our one-sample z statistic becomes a one-sample t statistic . By changing the denominator to be the standard error, our statistic no longer follows a Normal distribution. The t test statistic follows a t distribution with n – 1 degrees of freedom . One-Sample t Statistic n s μ x t n σ μ x z 0 0 - = - =
BPS - 5th Ed. Chapter 17 5 The t Distributions The t density curve is similar in shape to the standard Normal curve. They are both symmetric about 0 and bell-shaped. The spread of the t distributions is a bit greater than that of the standard Normal curve (i.e., the t curve is slightly “fatter”). As the degrees of freedom increase, the t density curve approaches the N (0, 1) curve more closely. This is because s estimates σ more accurately as the sample size increases.

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

View Full Document
BPS - 5th Ed. Chapter 17 6 The t Distributions
BPS - 5th Ed. Chapter 17 7 Using Table C Table C on page 693 gives critical values having upper tail probability p along with corresponding confidence level C . z * values are also displayed at the bottom .

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

View Full Document
BPS - 5th Ed. Chapter 17 8 Using Table C Find the value t * with probability 0.025 to its right under the t (7) density curve. t* = 2.365
BPS - 5th Ed. Chapter 17 9 This interval is exact when the population distribution is Normal and approximate for large n in other cases. where

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/27/2011 for the course MA 116 taught by Professor Muntheralraban during the Summer '11 term at Montgomery CC.

Page1 / 28

Chapter_17 - Chapter 17 Inference about a Population Mean...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online