The Cougar Swim Club acquired some Speedo Fastskin bodysuits and decided to test

Question

The Cougar Swim Club acquired some Speedo Fastskin bodysuits and decided to test them out. A number of the club's fastest swimmers performed a 50m freestyle swim in a regular spandex bodysuit and in a Speedo Fastskin suit. The table below summarizes their times in seconds (s) Swimmer spandex 31.1 28.9 31.4 34.9 27.7 36.7 33.3 30.8 Speedo Fastskin 29.1 30.4 25.3 31.7 28.2 32.9 28.6 26.2 2 4 8 Perform a t-test for dependent means to determine if there is a difference between the regular spandex suit and the Fastskin bodysuit in terms of performance Critical value of t use alpha = 0.05) Would you reject the null hypothesis?

Explanation / Answer

Ans:

Since the same participants competed in "both" events, the results are not independent. Use a paired t-test.

First find the difference between Fastskin and Spandex. Then calculate the descriptive statistics on the new column.

mean = 1.9625
std dev = 2.5065

t statistic = (1.9625 - 0) / (2.5065 / sqrt 8) = 2.215

df = 7

Critical value of t = (use alpha = 0.05) = 2.365

Would you reject the null hypothesis?

No,As t-statistic=2.215 < critical t

spandex Fastskin difference 1 31.1 29.1 2 2 28.9 30.4 -1.5 3 31.4 32 -0.6 4 34.9 31.7 3.2 5 27.7 28.2 -0.5 6 36.7 32.9 3.8 7 33.3 28.6 4.7 8 30.8 26.2 4.6 mean= 1.9625 std dev.= 2.5065

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