Question

The accompanying table shows the costs per ounce (in dollars) for a sample of toothpastes exhibiting very gcod stain removal, good stain removal, and fair stain removal. At a-005, there is evidence that at least one mean cost per cunce is diffe others. Perform a Schette Tost to determine which means have a signiticant difference Click here to view the toothpaste data and ANOVA table Toothpaste Data and ANOVA Table The critical value is Round to two decimal places as needed.) Very Good Good Fair The test statistic tor comparing the Very Good toothpaste to the Good toothpaste is Round to two decimal places as needed.) 0.46 0 49 0.41 0.37 0.47 0.51 065 0 45 058 043 0.74 0.59 0.46 The test statistic for comparing the Very Good toothpaste to the Far toothpaste is Round to two decimal places as needed.) The test statistic for comparing Round to two decimal places as needed.) g the Good toothpaste to the Fair toothpaste is Xeryood 0.452 xGoo,-0.608 Fair0450 Which means have a significant difference? Select all that apply A. Very Good and Good B. Very Good and Fair C. Good and Fair D. No specific pair of means is significantiy different Variation Sum of Squares Between rees of Freedom Mean Squares F 0 08217 0.08995 0 04109 0.00750 5 48 Within 12 Print Done

Answer 1

Significance Level(a) 0.05 From anova table, Between degrees of freedom (dfi) 2 Within degrees of freedom (df2) 12 Critical -value Between degrees of freedom Fa,dfi dfa (F0.05.2. 12-3.89 From F table ) 2 * F0.05.2, 12 2 * 3.89-7.96

Scheffe test statistic for comparing any two groups A and E (TA - TB)2 Tawhere n is sample size Here, TVery Good -0.452. -Good = 0.608. TFair-0.450 Very Good-6; TGood -5n Fair -4

MSWithin = 0.00750 from anova table Test statistic for comparing the very good toothpaste to good toothpaste (0.452- 0.608)2 050( Very Good TGood MSWithin nery Good Good -8.85 Test statistic for comparing the very good toothpaste to fair toothpaste (FVcry Good Fair) MSWin nvery Good nFair (0.452 - 0.450)2 Test statistic for comparing the good toothpaste to fair toothpaste (0.608 - 0.450)2 0.00750 +キ) GoodTFair 7.40 MSWithinHGnFir -) +

The only test statistic that is greater than the critical value is the test statistic for comparing the very good toothpaste and good toothpaste So, means having a significant difference is Very Good and Good