The Cougar Swim Club acquired some Speedo Fastskin bodysuits and decided to test
ID: 3434863 • Letter: T
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
Speedo Fastskin
1
31.1
29.1
2
28.9
30.4
3
31.4
25.3
4
34.9
31.7
5
27.7
28.2
6
30.8
26.2
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.
A) t= ?
B) df= ?
C) Critical Value of t =? (use alpha = 0.05)
D) Would you reject the null hypothesis?
Swimmer
spandex
Speedo Fastskin
1
31.1
29.1
2
28.9
30.4
3
31.4
25.3
4
34.9
31.7
5
27.7
28.2
6
30.8
26.2
Explanation / Answer
A) t= ?
t=mean difference/(s/vn)
=2.3167/(2.9294/sqrt(6))
=1.937166
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B) df= ?
The degree of freedom =n-1=6-1=5
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C) Critical Value of t =? (use alpha = 0.05)
It is a two-tailed test.
Given a=0.05, the critical values are t(0.025, df=5) = -2.57 or 2.57 (from student t table)
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D) Would you reject the null hypothesis?
Since t=1.937166 is between -2.57 and 2.57, we do not reject the null hypothesis.
30.8000 mean spandex 28.4833 mean Speedo Fastskin 2.3167 mean difference (spandex - Speedo Fastskin) 2.9294 std. dev. 1.1959 std. error 6 n 5 dfRelated Questions
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