Chapter 5.3-5.4

Chapter 5.3-5.4 - Statistics 511 Statistical Methods Dr...

Info iconThis preview shows pages 1–6. 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 Document Right Arrow Icon

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 Lecture 11: Random Samples Devore: Section 5.3-5.4 March, 2011 Page 1 Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 Definition of a Statistic • A statistic is any quantity whose value can be calculated from sample data. Prior to obtaining data, there is uncertainty as to what value of any particular statistic will result. • A statistic is a random variable denoted by an uppercase letter; a lowercase letter is used to represent the calculated or observed value of the statistic. March, 2011 Page 2 Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 • Example Consider a sample of n = 3 cars of a particular type; their fuel efficiencies may be x 1 = 30 . 7 mpg, x 2 = 29 . 4 mpg, x 3 = 31 . 1 mpg. • It may also be x 1 = 28 . 8 mpg, x 2 = 30 . mpg and x 3 = 31 . 1 mpg • This implies that the value of the mean ¯ X is different in these cases. Clearly, ¯ X is a statistic. The first sample has the mean ¯ X 1 = 30 . 4 mpg and the second one has ¯ X 2 ≈ 30 mpg March, 2011 Page 3 Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 Statistic Examples • A sample mean ¯ X of the sample X 1 ,...,X n is a statistic; ¯ x is one of its possible values • The value of the sample mean from any particular sample can be regarded as a point estimate of the population μ . • Another example is the sample standard deviation S , while s is its computed value • Yet another example is the difference between the sample means for two different populations ¯ X- ¯ Y March, 2011 Page 4 Statistics 511: Statistical Methods Dr. Levine Purdue University Spring 2011 Sampling distribution • Each statistic is a random variable and, as such, has its own distribution • Consider two samples of size n = 2 ; if X 1 = X 2 = 0 , ¯ X = 0 with probability P ( X 1 = 0 ∩ X 2 = 0)...
View Full Document

{[ snackBarMessage ]}

Page1 / 19

Chapter 5.3-5.4 - Statistics 511 Statistical Methods Dr...

This preview shows document pages 1 - 6. Sign up to view the full document.

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