Ted and Luke Thorndike have been approached by several local racquetball players, each of whom would like to be sponsored by Thorndike Sports Equipment during regional tournaments to be held during the next calendar year. In the past, Luke has resisted the sponsorship possibility. His philosophy has been, €œOur racquets are the best in the business. If they€™re smart, they€™ll use a Thorndike racquet; and if we€™re smart, we won€™t give it to them for free.€
It wasn€™t easy, but Ted finally convinced Luke of the benefits to be gained by exposing racquet club members and tournament spectators to high-caliber players who rely on Thorndike racquets and related sports equipment. According to Ted, this exposure is easily worth a few racquets, a couple of pairs of court shoes, and a half-dozen €œThorndike Power€ T-shirts.
The Thorndikes compromise between Luke€™s original idea of sponsoring nobody and Ted€™s proposal to sponsor at least three players. Their eventual selection is Kermit Clawson, an outstanding young player who finished third in the regional championship tournament last year. Kermit and the Thorndikes have reached agreement on all of the details of the sponsorship arrangement but must decide on which combination of racquet and string would be best.
Kermit is a power player who relies heavily on the speed of his serves and return shots. The Thorndike line currently includes four €œpower€ racquets, each of which can be strung with one of three types of string most often used by strong hitters like Kermit. Ted sets up a test in which Kermit will hit two €œpower serves€ with each combination of racquet and string. The 24 serves will be made in a random order, and each will be clocked with a radar gun. Besides helping Kermit select the combination he likes best, the test will also help the Thorndikes study what Ted has referred to as the €œmain€ and €œinteractive€ effects of the racquets and strings. The data from the test are shown here and are provided in file THORN12.
From these data, which combination of racquet and string would you recommend that Kermit use? Also, employ the appropriate ANOVA procedure in helping Ted respond to Luke€™s statement that €œthe racquets are all the same, the strings are all the same, and it doesn€™t matter which string goes into which racquet.€

Racquet 2 4 105, 108 110, 108 113, 112 113, 109 109, 107 114, 109 114, 112 118, 114 114, 114 109, 108 mph 113, 113 110, 107 String 3