Find${\mathbf{\chi }}_{\frac{\mathbf{\alpha }}{\mathbf{2}}}^{\mathbf{2}} \mathbf{and} {\mathbf{\chi }}_{\mathbf{1}\mathbf{-}\frac{\mathbf{\alpha }}{\mathbf{2}}}^{\mathbf{2}}$from Table IV, Appendix D, for each of the following:

a. n = 10, = .05

b. n = 20, = .05

c. n = 50, = .01

Chi-square distribution is a statistical distribution used for hypothesis testing The graphs of this distribution are dependent on the degrees of freedom. They also help in checking the goodness of fit and independence of variables.

By referring to the chi-square distribution table, we have to compute the probability,

For n = 10, $\alpha$ = .05, the value is:

${\chi }_{\frac{\alpha }{2}}^2=19.0228, {\chi }_{1-\frac{\alpha }{2}}^2=2.70039$

Therefore, the answer is: 19.0228, 2.70039

By referring to the chi-square distribution table, we have to compute the probability,

For n = 20, $\alpha$= .05, the value is:

${\chi }_{\frac{\alpha }{2}}^2=32.8523, {\chi }_{1-\frac{\alpha }{2}}^2=8.90655$

Therefore, the answer is: 32.8523; 8.90655

By referring to the chi-square distribution table, we have to compute the probability,

For n = 50, = .01, the value is:

${\chi }_{\frac{\alpha }{2}}^2=79.49, {\chi }_{1-\frac{\alpha }{2}}^2=27.9907$

Therefore, the answer is: 79.49; 27.9907