14. Statistical Techniques in Business & Economics (12)

12 ­ © 2004 by The McGraw­Hill Companies, Inc. All rights reserved. 12 ­ 2 When you have completed this chapter, you will be able to: 1. Discuss the general idea of analysis of variance. 2. List the characteristics of the F distribution. Conduct a test of hypothesis to determine whether the . 3 variances of two populations are equal. 4. Organize data into a one­way and a . two­way ANOVA tableCopyright © 2004 by The McGraw­Hill Companies, Inc. All rights reserved. 12 ­ 3. 5. Define the terms treatments and blocks. 6. Conduct a test of hypothesis to determine whether . three or more treatment means are equal Develop multiple tests for difference between each pair . 7. of treatment meansCopyright © 2004 by The McGraw­Hill Companies, Inc. All rights reserved. Characteristics of the . Characteristics of the . 12 ­ 4 F­Distribution . F­Distribution . There is a “family of F­Distributions:. There is a “family of F­Distributions:. Each member of the family is determined by . two parameters: . the numerator degrees of freedom, and the . denominator degrees of freedom. F cannot be negative, and it is a continuous distribution. The F distribution is positively skewed. Its values range from 0 to as F , the . curve approaches the X­axisCopyright © 2004 by The McGraw­Hill Companies, Inc. All rights reserved. 12 ­ 5. Test for Equal Variances. Test for Equal Variances. For the two tailed test, the test statistic . is given by:. 2. s1. F. s 22 s 12 and are the sample variances . s 22 for the two samples The null hypothesis is rejected . if the computed value of the test statistic . is greater than the critical valueCopyright © 2004 by The McGraw­Hill Companies, Inc. All rights reserved. 12 ­ 6. Colin, a stockbroker at Critical Securities, . reported that the mean rate of return on . a sample of 10 internet stocks was percent . with a standard deviation of percent. . The mean rate of return on a sample of 8 utility stocks . was percent with a . standard deviation of percent. . At the .05 significance level, . can Colin conclude that the