An online survey by the Sporting Goods Manufacturers Association, a trade group of sports retailers and marketers, claimed that household income of recreational athletes varies by sport (The Wall Street Journal, August 10, 2009). In order to verify this claim, an economist samples five sports enthusiasts participating in each of six different recreational sports and obtains each enthusiast’s income (in $1,000s), as shown in the accompanying table.

a. Specify the competing hypotheses in order to test the association’s claim .
b. Create an ANOVA table. Assume incomes are normally distributed.
c. At the 5% significance level, what is the critical value?
d. Do some average incomes differ depending on the recreational sport?Explain.

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On-road Off-road Snorkeling Sailing Windsurfing Bowling Triathlon Triathlon Boardsailing/ 87.6 95.0 94.6 98.8 87.2 82.5 90.9 86.0 93.6 75.9 75.6 83.1 74.4 80.5 石= 77.9 79.3 64.547.7 75.8 67.2 59.6 79.6 62.868.0 78.5 59.2 60.9 73.2 66.550.9 |저 = 77.3| xs = 64.0 |Xs = 57.4 98.4 Xi = 93.5 № = 89.4| 28.8 -28.5 -13.8-74s-10366.4 x = 76.6