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Lecture Statistical techniques in business and economics - Chapter 12: Analysis of variance

When you finish this chapter, you should be able to: Discuss the general idea of analysis of variance, discuss the general idea of analysis of variance, conduct a test of hypothesis to determine whether the variances of two populations are equal, organize data into a one-way and a two-way ANOVA table. | Chapter 12 Analysis of Variance 1. Discuss the general idea of analysis of variance. 2. List the characteristics of the F distribution. Chapter Goals When you have completed this chapter, you will be able to: Organize data into a one-way and a two-way ANOVA table. 3. Conduct a test of hypothesis to determine whether the variances of two populations are equal. 4. and. 5. Define the terms treatments and blocks. 6. Conduct a test of hypothesis to determine whether three or more treatment means are equal. Chapter Goals 7. Develop multiple tests for difference between each pair of treatment means. Characteristics of the F-Distribution There is a “family of F-Distributions: 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 X-axis Test for Equal . | Chapter 12 Analysis of Variance 1. Discuss the general idea of analysis of variance. 2. List the characteristics of the F distribution. Chapter Goals When you have completed this chapter, you will be able to: Organize data into a one-way and a two-way ANOVA table. 3. Conduct a test of hypothesis to determine whether the variances of two populations are equal. 4. and. 5. Define the terms treatments and blocks. 6. Conduct a test of hypothesis to determine whether three or more treatment means are equal. Chapter Goals 7. Develop multiple tests for difference between each pair of treatment means. Characteristics of the F-Distribution There is a “family of F-Distributions: 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 X-axis Test for Equal Variances For the two tailed test, the test statistic is given by: The null hypothesis is rejected if the computed value of the test statistic is greater than the critical value where and are the sample variances for the two samples 2 1 s 2 2 s Colin, a stockbroker at Critical Securities, reported that the mean rate of return on a sample of 10 internet stocks was 12.6 percent with a standard deviation of 3.9 percent. Q uestion The mean rate of return on a sample of 8 utility stocks was 10.9 percent with a standard deviation of 3.5 percent. At the .05 significance level, can Colin conclude that there is more variation in the internet stocks? Solve Do not reject H0 Reject H0 and accept H1 State the null and alternate hypotheses Step 1 Select the level of significance Step 2 Identify the test statistic Step 3 State the decision rule Step 4 Step 5 Hypothesis Testing Compute the value of the test statistic and make a decision Recall Hypothesis Test State the null and alternate hypotheses .