Ted and Luke Thorndike have just returned from lunch with Candice Ergonne, president of a chain of 550 health clubs located across the United States. The clubs have a quality image and are known for featuring equipment and facilities that are second to none. The Thorndikes are rightfully pleased that Ms. Ergonne has invited their proposal for supplying exercise bicycles to the 120 new clubs that are to be opened during the next year.
After further negotiations, the deal is practically closed, but some fine-tuning remains with regard to the seat design for the €œThornBike 2000€ model that has been selected. Ms. Ergonne recognizes that some club members require wider seats than others but doesn€™t want to call attention to this fact by having differing seat widths from one bike to the next. She would much prefer a €œone size fits all€ approach to the seating decision.
In an experiment to evaluate four seat designs, Ms. Ergonne supplies seven persons who vary widely in size, while the Thorndikes provide the seats to be tested. Each of the individuals spends 5 minutes riding on each of the four seat designs, with the order determined randomly. The subject then rates the comfort of the seat on a scale of 1 to 10, with 1 = €œpoor€ and 10 = €œexcellent.€ The results are as shown below. The data are also in file THORN14.
From these results, and using the 0.10 level of significance, can Ted Thorndike reject the null hypothesis that the four seating designs could be equally comfortable?

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