hw5solution - stat 226 homework 5 Answer Key 1 Why Why do...

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: stat 226 homework 5 Answer Key 1. Why? - Why do we need to do this???? While ¯ x as a point estimate is unbiased (on average it will estimate the population mean correctly) it will rarely equal the value of the unknown population mean μ . Our estimate often will be close to μ but the estimate does not provide any information on how close it will be to μ . A confidence interval allows us not only to incorporate the variability of our sample estimator ¯ x (how much does ¯ x usually vary about the unknown population mean μ ) but also to attach a level of confidence. We are able to make a statement how confident we can be that the population mean μ will be contained in the obtained confidence interval. In general, a point estimator is never considered very informative without providing any information of how much variability is associated with this estimator. 2. Critical Values. (a) z * = 1 . 02 (b) z * = 1 . 75 (c) z * = 2 . 17 (d) As the level of confidence increases so does the value of z * . This should make sense intuitively because z * contributes to the width of confidence interval. A larger z * value will cause the interval to get wider which in turn yields more confidence that the interval indeed captures the unknown population mean. 3. Confidence Intervals. (a) ¯ x ± z * σ √ n ⇒ 50 ± 1 . 02 10 √ 25 ⇒ 50 ± 2 . 04 ⇒ (47 . 96 , 52 . 04) (b) ¯ x ± z * σ √ n ⇒ 50 ± 1 . 75 10 √ 25 ⇒ 50 ± 3 . 50 ⇒ (46 . 50 , 53 . 50) (c) ¯ x ± z * σ √ n ⇒ 50 ± 2 . 17 10 √ 25 ⇒ 50 ± 4 . 34 ⇒ (45 . 66 , 54 . 34) (d) As the confidence level increases, the width of the interval also increases. The only thing that changes is the critical value, which gets larger with higher confidence levels (See 2.(d))....
View Full Document

This note was uploaded on 05/05/2010 for the course STAT 226 taught by Professor Abbey during the Fall '08 term at Iowa State.

Page1 / 4

hw5solution - stat 226 homework 5 Answer Key 1 Why Why do...

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