Two-Way ANOVA Analysis Without Replication

Problem

What if you want to know if there is a difference in driving distance between three brands of golf balls for different golfers?

The goal is to accept or reject the null hypothesis (i.e., the samples have different means) at a certain confidence level (95% or 99%).

The data: Golfer Brand A Brand B Brand C Woods 250 255 262 Jones 225 235 230 Smith 270 282 285 Carroll 235 240 246 Reed 215 220 223