Option B [tex]n_{1} = 27 ,n_{2} = 29[/tex] are the two sample sizes cannot be true.
HYPOTHESIS TEST
Given that:
The degree of freedom for the test of two independent population means is 56.
Degrees of freedom for two independent populations are well known.
[tex]n_{1} + n_{2} - 2[/tex]
[tex]n_{1} + n_{2} - 2[/tex] = 56
[tex]n_{1} + n_{2}[/tex] = 54
Total sample sizes = 54
Option B ( [tex]n_{1} = 27 ,n_{2} = 29[/tex] ) cannot be true.
To learn more about hypothesis testing check the given link
https://brainly.com/question/14587073
#SPJ4