Answer
Step 1:
$H_0$ : The class of vertebrate are independent from whether it is endangered or threatened species.
$H_1$: The class of vertebrate are dependent upon whether it is endangered or threatened species.
Step 2:
Since α=0.05, the critical value using Table G with (2-1)(5-1) = (1)(4) =4 degrees of freedom is 9.488.
If α=0.01, df = 4, critical value = 13.277.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(247)(81)}{(369)}$ = 54.22
$E_1,2$ = $\frac{(247)(91)}{(369)}$ = 60.91
$E_1,3$ = $\frac{(247)(37)}{(369)}$= 24.77
$E_1,4$ = $\frac{(247)(23)}{(369)}$ = 15.40
$E_1,5$ = $\frac{(247)(137)}{(369)}$ = 91.70
$E_2,1$ = $\frac{(122)(81)}{(369)}$ = 26.78
$E_2,2$ = $\frac{(122)(91)}{(369)}$ = 30.09
$E_2,3$ = $\frac{(122)(37)}{(369)}$ = 12.23
$E_2,4$ = $\frac{(122)(23)}{(369)}$ = 7.60
$E_2,5$ = $\frac{(122)(137)}{(369)}$ = 45.30
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(68-54.22)^{2}}{54.22}$ + $\frac{(76-60.91)^{2}}{60.91}$ + $\frac{(14-24.77)^{2}}{24.77}$ + $\frac{(13-15.40)^{2}}{15.40}$ + $\frac{(76-91.70)^{2}}{91.70}$ + $\frac{(13-26.78)^{2}}{26.78}$ + $\frac{(15-30.09)^{2}}{30.09}$ + $\frac{(23-12.23)^{2}}{12.23}$ + $\frac{(10-7.60)^{2}}{7.60}$ + $\frac{(61-45.30)^{2}}{45.30}$
=3.502+3.737+4.681+0.373+0.689+7.091+7.565+9.477+0.755+5.445
=45.314
Step 4:
Since 45.314 > 13.277, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that the class of vertebrate are dependent upon whether it is endangered or threatened species.
