Answer
10.
Step 1:
$H_0$ : The rank of officers in the military is independent from the branch of the Armed Forces.
$H_1$: The rank of officers in the military is dependent upon the branch of the Armed Forces.
Step 2:
Since α=0.05, the critical value using Table G with (4-1)(2-1) = (3)(1) =3 degrees of freedom is 7.815.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(73282)(31358)}{(200468)}$ = 11463.06
$E_1,2$ = $\frac{(73282)(169110)}{(200468)}$ = 61818.94
$E_2,1$ = $\frac{(50566)(31358)}{(200468)}$= 7909.73
$E_2,2$ = $\frac{(50566)(169110)}{(200468)}$ = 42656.27
$E_3,1$ = $\frac{(10457)(31358)}{(200468)}$ = 1635.73
$E_3,2$ = $\frac{(10457)(169110)}{(200468)}$ = 8821.27
$E_4,1$ = $\frac{(66163)(31358)}{(200468)}$ = 10349.48
$E_4,2$ = $\frac{(66163)(169110)}{(200468)}$ = 55813.52
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(10791-11.463.06)^{2}}{11463.06}$ + $\frac{(62491-61818.94)^{2}}{61818.94}$ + $\frac{(7816-7909.73)^{2}}{7909.73}$ + $\frac{(42750-42656.27)^{2}}{45656.27}$ + $\frac{(932-1635.73)^{2}}{1635.73}$ + $\frac{(9525-8821.27)^{2}}{8821.27}$ + $\frac{(11819-10349.48)^{2}}{10349.48}$ + $\frac{(54344-55813.52)^{2}}{55813.52}$
=39.402+7.306+1.111+0.206+302.758+56.140+208.657+38.691
=654.272
Step 4:
Since 654.272 > 7.815, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that the rank of officers in the military is dependent upon the branch of the Armed Forces.
