SECTION 10.4 Analysis of Variance 569 17. Grade Point Average A study was conducted in which a sample of 24 high school students was asked to give their grade point average (GPA). The block design shows the GPAs of male and female students from four different age groups. Male 2.5, 2.1, 3.8 Female 4.0, 2.1, 1.9 15 4.0, 1.4, 2.0 3.5, 3.0, 2.1 16 17 18 3.5, 2.2, 2.0 4.0, 2.2, 1.7 3.1, 0.7, 2.8 1.6, 2.5, 3.6 Gender Age 18. Laptop Repairs The manager of a computer repair service wants to determine whether there is a difference in the time it takes four technicians to repair different brands of laptops. The block design shows the times (in minutes) it took for each technician to repair three laptops of each brand. Brand A 67, 82, 64 42, 56, 39 69, 47, 38 44, 62, 55 47, 58, 62 55, 45, 66 70, 44, 50 47, 29, 40 Brand B 47, 36, 68 39, 74, 51 74, 80, 70 45, 62, 59 Brand C Technician 1 Technician 2 Technician 3 Technician 4 Brand Technician The Scheffé Test If the null hypothesis is rejected in a one-way ANOVA test of three or more means, then a Scheffé Test can be performed to find which means have a significant difference. In a Scheffé Test, the means are compared two at a time. For instance, with three means you would have these comparisons: x1 versus x2, x1 versus x3, and x2 versus x3. For each comparison, calculate 1xa - xb2 2 SSW Σ1ni - 12 a 1 na + 1 nbb where xa and xb are the means being compared and na and nb are the corresponding sample sizes. Calculate the critical value by multiplying the critical value of the one-way ANOVA test by k - 1. Then compare the value that is calculated using the formula above with the critical value. The means have a significant difference when the value calculated using the formula above is greater than the critical value. Use the information above to solve Exercises 19 –22. 19. Refer to the data in Exercise 7. At a = 0.01, perform a Scheffé Test to determine which means have a significant difference. 20. Refer to the data in Exercise 8. At a = 0.01, perform a Scheffé Test to determine which means have a significant difference. 21. Refer to the data in Exercise 10. At a = 0.01, perform a Scheffé Test to determine which means have a significant difference. 22. Refer to the data in Exercise 11. At a = 0.10, perform a Scheffé Test to determine which means have a significant difference.
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