Question 250041: A teacher wishes to compare two different groups of students with respect to their mean time to complete a standardized test. The time required is determined for each group. The data summary is given below. Test the claim at a= 0.10, that there is no difference in variance. Give the critical region, test statistic value, and conclusion for the F test.
n1 = 24 s1 = 21
n2 = 40 s2 = 39
a = 0.10
· State the null and alternate hypotheses
· Determine which test statistic applies, and calculate it
· Determine the critical region
· State your decision: Should the null hypothesis be rejected?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A teacher wishes to compare two different groups of students with respect to their mean time to complete a standardized test. The time required is determined for each group. The data summary is given below.
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Test the claim at a= 0.10, that there is no difference in variance. Give the critical region, test statistic value, and conclusion for the F test.
n1 = 24 s1 = 21
n2 = 40 s2 = 39
a = 0.10
· State the null and alternate hypotheses
Ho: sigma1^2 -sigma2^2 = 0
H1: sigma1^2 - sigma2^2 is not zero
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· Determine which test statistic applies, and calculate it
F = 21^2/39^2 = 0.2899
p = 0.0025
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· Determine the critical region
Right Tail:Fcrit = F(0.05,n1-1,n2-1) = F(0.05,23,39) = 3.84
Reject Ho if the test statistic is greater than 2.18
Left Tail: Fcrit = F(0.05,n2-1,n1-1)= F(0.05,39,23) = 2.53
Reject Ho if the test statistic is less than 2.53
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· State your decision: Should the null hypothesis be rejected?
The test stat is in the reject interval so reject Ho.
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Cheers,
Stan H.
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