2. The Speedo LZR Racer Suit is a high-end, body-length swimsuit that was launched on February 13, 2008. When 17 world records fell at the December 2008 European Short Course Championships in Croatia, many believed a modification in the rules surrounding swimsuits was necessary. The FINA Congress, the international governing board for swimming, banned the LZR Racer and all other body-length swimsuits from competition, effective January 2010. In a statement to the public, FINA defended its position with the following statement: "FINA wishes to recall the main and core principle that swimming is a sport essentially based on the physical performance of the athlete" (BBC Sport, March 14, 2009).
Luke Johnson, a freelance journalist, wonders if the decision made by FINA has statistical backing. He conducts an experiment with the local university's Division I swim team. He times 10 of the swimmers swimming the 50-meter breaststroke in his/her bathing suit and then retests them while wearing the LZR Racer. The results are saved in "LZR_Racer" of Chapter10.xlsx.
In a report, use the sample information to
a. Determine whether the LZR Racer improves swimmers' times at the 5% significance level. Assume that the time difference is normally distributed.
b. Comment on whether the data appear to support FINA's decision.
Swimmer Time in Bathing Suit Time in LZR Racer
1 27.64 27.45
2 27.97 28.06
3 29.04 28.84
4 29.85 29.63
5 30.12 30.18
6 32.73 32.71
7 33.32 32.87
8 35.36 35.21
9 37.34 37.11
10 38.08 37.93
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