Producers of a new grass seed called Pearl's Premium claim that grass grown using its seed blend requires less maintenance as compared to other brands (The Boston Globe, July 4, 2009). For instance, grass grown using Pearl's Premium needs mowing only once a month. Suppose an independent tester wants to test whether the average height of grass after one month's growth is the same between Pearl's Premium and the other two top-selling brands. The independent tester measures 25 grass blades using each of 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

a. At the 5% significance level, can we conclude that the average heights of grass blades differ by brand?
b. If significant differences exist, use Tukey's HSD method at the 5% significance level to determine which brands differ.

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Source of Variation SS df MS F p-value Fcri Between 64.43 2 32.21 121.67 8.09E-24 3.123 Groups Within 19.06 72 0.26 Groups Total 83.49 74