ComparingTwoPopulations-solutionsPart-a

ComparingTwoPopulations-solutionsPart-a - Comparing two...

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

View Full Document Right Arrow Icon
Comparing two populations or processes 1 Introduction In previous chapters, we introduced models for a characteristic of units in a population, models for a process, and developed procedures (conFdence intervals & hypothesis tests) to make inference for the parameters (e.g. μ & θ ) of these models using data. In this chapter, we will compare a characteristic of the units in two populations: This characteristic of the units in population 1 is modeled with a distribution with mean μ 1 and standard deviation σ 1 . This characteristic of the units in population 2 is modeled with a distribution with mean μ 2 and standard deviation σ 2 . We will introduce procedures (conFdence intervals & hypothesis tests) to make infer- ence for the di±erence: μ 1 - μ 2 , which itself is a parameter, using data. (e.g. is there statistical evidence that μ 1 - μ 2 > 0). These methods also apply to the comparison of two processes. Procedures to compare σ 1 and σ 2 will be introduced in a supplement available on Moodle. 2 Unpaired comparisons: the two independent sam- ples t-test and confdence interval For μ 1 - μ 2 Examples oF unpaired comparisons oF means Compare the mean starting salary of graduates of UMN–TC with graduates from Ohio State. Compare the mean lifetime of Duracell Batteries with that of Energizer batteries. Compare the mean LDL cholesterol reduction of those given a new treatment (treated) with those given the present treatment (control). 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
2.1 Two independent samples from two Normal distributions Population/Process 1’s sample measurements x 1 , . . . , x n 1 are a realization of a random sample of size n 1 from N ( μ 1 , σ ). Let ¯ x & s 1 denote the observed sample mean & standard deviation. Population/Process 2’s sample measurements y 1 , . . . , y n 2 are a realization of a random sample of size n 2 from N ( μ 2 , σ ). Let ¯ y & s 2 denote the observed sample mean & standard deviation. The two random samples are independent . The quantity ¯ x - ¯ y is an estimate of μ 1 - μ 2 . The quantity s p , deFned as: s p = r ( n 1 - 1) s 2 1 + ( n 2 - 1) s 2 2 n 1 + n 2 - 2 is an estimate of σ . This is a realization of the estimator S p . We are assuming that Population/Process 1’s distribution has the same standard deviation σ as Population/Process 2’s distribution. Example 2.1: Suppose we wish to compare the mean lifetimes (in hours) of two types of batteries (Brand A and Brand B). We acquire 5 brand A batteries and measure lifetimes in a portable CD player: 10 . 5 , 9 . 6 , 10 . 2 , 9 . 9 , 10 . 4 We also acquire 6 brand B batteries and measure lifetimes in a portable CD player: 8 . 9 , 9 . 4 , 9 . 7 , 9 . 3 , 8 . 8 , 10 . 0 Assume that brand A battery lifetimes: x 1 , . . . , x 5 are a realization of a random sample from N ( μ 1 , σ ) and brand B battery lifetimes: y 1 , . . . , y 6 are a realization of an independent random sample from N ( μ 2 , σ ). Using the data, compute estimates for μ 1 - μ 2 , and σ .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/06/2011 for the course STAT 5021 taught by Professor Staff during the Spring '08 term at Minnesota.

Page1 / 9

ComparingTwoPopulations-solutionsPart-a - Comparing two...

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

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