Respuesta :
The critical f-value using two tailed test is [tex]F_{\frac{\alpha }{2} }=6.26[/tex] and [tex]F_{(1-\frac{\alpha }{2} )}=0.19[/tex].
In this question,
The sample size for the numerator = 6
The sample size for the denominator = 5
The significance level is α = 0.10
For two tailed test, α/2 = 0.05
For [tex]F_{(1-\frac{\alpha }{2} )}=0.95[/tex]
The degrees of freedom of numerator is
[tex]df_{num} = 6-1[/tex]
⇒ 5
The degrees of freedom of denominator is
[tex]df_{denom} = 5-1[/tex]
⇒ 4
Now consider the f-distribution table and find the value that corresponds to the degrees of freedom of numerator 5 and the degrees of freedom of denominator 4.
For two tailed test, the corresponding upper critical f-value is
⇒ [tex]F_{\frac{\alpha }{2} }=6.26[/tex]
Now, the corresponding lower critical f-value is
⇒ [tex]F_{(1-\frac{\alpha }{2} )}=0.19[/tex]
Hence we can conclude that the critical f-value using two tailed test is [tex]F_{\frac{\alpha }{2} }=6.26[/tex] and [tex]F_{(1-\frac{\alpha }{2} )}=0.19[/tex].
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