Producers of a new grass seed called Pearl's Premium claim th at grass grown using its seed blend requires less m aintenance as compared to other brands (The Boston Globe, July 4 , 2009). For instance, grass grown using Pearl's Premium needs m ow ing only once a m onth. Suppose an independent tester wants to test w hether the average height of grass after one month's grow th is the same betw een Pearl's Premium and the other tw o top-selling brands. The independent tester measures 25 grass blades using each o f the three seeds (glass blades are measured in inches).
Using Excel, he constructs the following ANOVA table with supporting descriptive statistics.
SUMMARY Groups Count Average Pearl's Premium 25 4.83 Top Brand 1 25 6.50 Top Brand 2 25 6.99 ANOVA Source of Variation SS df MS F p-value F crit Between Groups 64.43 2 32.21 121.67 8.09E-24 3.123 Within Groups 19.06 72 0.26 Total 83.49 74

a. At the 5% significance level, can we conclude that the average heights of grass blades differ by brand?

b. If sign ificant d ifferences exist, use Tukey's m e th o d at th e 5% significance level to d e te rm in e w hich brands differ. P-69