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

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SUMMARY

The discussion centers on calculating the absolute value of the t statistic for a one-sided test involving two variances. The null hypothesis states that (sigma1)^2 >= (sigma2)^2, while the alternative hypothesis asserts that (sigma1)^2 < (sigma2)^2. Given the sample sizes n1 = 8, n2 = 10, and standard deviations s1 = 13.0, s2 = 11.5, the correct test statistic for the F test is determined to be 1.278. The absolute value of the t statistic is derived from the square root of the F statistic, confirming the relationship between these statistical measures.

PREREQUISITES
  • Understanding of hypothesis testing, specifically for variances
  • F-distribution and its application in statistical tests
  • Knowledge of calculating test statistics, including F and t statistics
  • Familiarity with one-sided tests in statistical analysis
NEXT STEPS
  • Study the derivation of the F statistic in hypothesis testing
  • Learn about the relationship between F and t distributions
  • Explore one-sided vs. two-sided tests in statistical analysis
  • Review practical applications of variance testing in real-world scenarios
USEFUL FOR

This discussion is beneficial for statisticians, data analysts, and researchers involved in hypothesis testing and variance analysis, particularly those working with F and t statistics in their studies.

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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