The Cougar Swim Club acquired some Speedo Fastskin bodysuits

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?

Solution

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.