What is the absolute value of the t statistic for the one-sided test?

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The discussion focuses on calculating the test statistic for an F-test given the null hypothesis that the variance of one population is greater than or equal to that of another. The correct test statistic is identified as 1.278. There is a consideration of switching the sample standard deviations in the F-statistic equation to create an upper-tail test, resulting in a test statistic of 0.783. It is noted that the absolute value of the t statistic for the one-sided test is the square root of the F statistic. The conversation emphasizes the relationship between the F and t statistics in hypothesis testing.
student007
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Consider the test of the hypotheses:
Null: (sigma1)^2>=(sigma2)^2
Alternative: (sigma1)^2<(sigma2)^2
where α = 0.05 and:
n1 = 8 and s1 = 13.0
n2 = 10 and s2 = 11.5.
What is the test statistic for F?

Your Answer:
1.278
Correct Answer:
1.278

If the alternative hypothesis for two variances has "<", couldn't you switch the s1 and s2 in the f-stat equation to create an upper-tail test? if so, my test statistic would be 0.783
 
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F test is a one-sided test. The square root of the F statistic is the absolute value of the t statistic for the one-sided test.
 

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