Help, I\'m studying for a test but I can\'t figure out how to work this one: In

Question

Help, I'm studying for a test but I can't figure out how to work this one:

In swimming, clearly you would like to swim fast, but swimming consistent times is also important. A survey of 34 swims by men on a local university's swim team found a variance of their swimming times was 3 seconds. A similar survey of 27 swims by swimmers at a different university found the variance was 9 seconds. When testing the hypothesis (at the 5% level of significance) that the variances are equal, what is the test statistic? (please round your answer to 2 decimal places)

CORRECT ANSWER IS 3.00

Explanation / Answer

We use F-test for checking hypothesis that the variances of 2 samples are equal.

H0: 12= 22

Now, sample 1 has variance 3 and number of obs 34 => degrees of freedom = 34 - 1 = 33

sample 2 has variance 9 and no. of obs 27 => degrees of freedom = 27 - 1 = 26

now, f-stat = s12  / s22   = 9/3 = 3 (answer) with df1 = 26 and df2 = 33

Now, critical f-stat for above df1 and df2 = 1.85 (approx.)

Since, f-stat > f-critical, we reject the null hypothesis

i.e. there is no reasonable evidence to say that variance of the 2 samples are equal.

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