LESSON 17 THE FDISTRIBUTION Outline The Fdistribution 1

LESSON 17: THE F-DISTRIBUTION Outline • The F-distribution 1

THE F-DISTRIBUTION • If you have two populations, and if you want to know if two populations have an identical variance, use F-distribution if each population has a normal distribution. • The F-distribution also uses sample variance to make an inference about population variance. The F-distribution is used to compare the variances of two samples. 2

THE F-DISTRIBUTION • Consider any two normally distributed populations • Let = variance of a sample of size drawn from • The F-statistic is as follows: and 3

THE F-DISTRIBUTION • The F-distribution is positively skewed and its shape depends on two parameters – Degrees of freedom for numerator = – Degrees of freedom for denominator = 4

THE F-DISTRIBUTION • For each upper-tail probability such that , there is a critical value • A large F-square statistic is usually undesirable. It is inferred at significance level that two population do not have an identical variance if 5

THE F-DISTRIBUTION • Table J, Appendix A, pp. 546 -553 gives the critical values F. 05 (lightface) and F. 01 (boldface) for various numerator and denominator degrees of freedoms. • The relevant Excel commands are FDIST and FINV • FDIST (critical value, d. f. numerator, d. f. denominator) returns the upper tail area • FINV (upper tail area, d. f. numerator, d. f. denominator) returns the critical chi-square value. Thus, FINV does the same job as Table J. 6

THE F-DISTRIBUTION Example 1: Determine the critical values for the F-statistic in the following cases: a. b. 7

THE F-DISTRIBUTION Example 2: Does the following two population have an identical variance at 5% level of significance? 8

THE F-DISTRIBUTION Example 3: Does the following two population have an identical variance at 5% level of significance? 9

READING AND EXERCISES Lesson 17 Reading: Section 9 -6, pp. 289 -291 Exercises: 9 -41, 9 -42 10