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Bennie Waller wallerbd@longwood 434-395-2046

Bennie Waller wallerbd@longwood.edu 434-395-2046 Longwood University 201 High Street Farmville, VA 23901. Bennie Waller wallerbd@longwood.edu 434-395-2046 Longwood University 201 High Street Farmville, VA 23901. The F Distribution. It is

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Bennie Waller wallerbd@longwood 434-395-2046

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  1. Bennie Waller wallerbd@longwood.edu 434-395-2046 Longwood University201 High StreetFarmville, VA 23901

  2. Bennie Waller wallerbd@longwood.edu 434-395-2046 Longwood University201 High StreetFarmville, VA 23901

  3. The F Distribution • It is • used to test whether two samples have equal variances • used to compare the means of more than two populations simultaneously. The simultaneous comparison of several population means is called analysis of variance(ANOVA).

  4. The F Distribution H0: µ1 = µ2 =…= µk H1: The means are not all equal • H0: σ12 = σ22 • H1: σ12≠σ22

  5. ANOVA Test for Equal Variances - Example Step 1: The hypotheses are: H0: σ12 = σ22 H1: σ12≠σ22 Step 2: The significance level is .10. Step 3: The test statistic is the F distribution. 12-5

  6. ANOVA Test for Equal Variances - Example Step 4: State the decision rule. Reject H0 ifF > F/2,v1,v2 F > F.10/2,7-1,8-1 F > F.05,6,7 12-6

  7. Consider the following example of travel times on different routes See example in spreadsheet “VARanova” tab

  8. B A

  9. ANOVA Comparing Means of Two or More Populations • TheNull Hypothesis is that the population means are all the same. The Alternative Hypothesis is that at least one of the means is different. • TheTest Statistic is the F distribution. • TheDecision rule is to reject the null hypothesis if F (computed) is greater than F (table) with numerator and denominator degrees of freedom. • Hypothesis Setup and Decision Rule: H0: µ1 = µ2 =…= µk H1: The means are not all equal Reject H0 if F > F,k-1,n-k 12-9

  10. ANOVA Analysis of Variance – F statistic • If there are k populations being sampled, the numerator degrees of freedom is k – 1. • If there are a total of n observations the denominator degrees of freedom is n – k. • The test statistic is computed by: 12-10

  11. Consider the following example comparing the difference in means of three groups NOTICE THE DIFFERENCE IN VARIATION ACROSS GROUPS RELATIVE TO WITHIN GROUPS See example in spreadsheet “ANOVAMeans” tab

  12. Problem: A company compared the variance of salaries for employees who have been employed for 5 years or less with employees who have been employed for 10 years or more. They randomly selected 21 employees with 5 years or less experience and 15 employees with 10 years or more experience. The standard deviation for the group with 5 years or less experience was $2,225; the standard deviation for the group with 10 years or more experience is $1,875. Using the 0.05 significance level, what is the decision regarding the null hypothesis? 

  13. 44. Given the following Analysis of Variance table for three treatments each with six observations. Given the following Analysis of Variance table for three treatments each with six observations. What is the decision regarding the null hypothesis?

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