Answer
Step 1:
$H_0$ : The malls and the proportions of customers who are willing to participate in a marketing research survey are independent from each other.
$H_1$: The malls and the proportions of customers who are willing to participate in a marketing research survey are dependent upon each other.
Step 2:
Since α=0.01, the critical value using Table G with (2-1)(3-1) = (1)(2) =2 degrees of freedom is 9.210.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(133)(92)}{(276)}$ = 44.33
$E_1,2$ = $\frac{(133)(92)}{(276)}$= 44.33
$E_1,3$ = $\frac{(143)(92)}{(276)}$= 44.33
$E_2,1$ = $\frac{(143)(92)}{(276)}$ = 47.67
$E_2,2$ = $\frac{(143)(92)}{(276)}$ = 47.67
$E_2,3$ = $\frac{(143)(92)}{(276)}$ = 47.67
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(52-44.33)^{2}}{44.33}$ + $\frac{(45-44.33)^{2}}{44.33}$ + $\frac{(36-44.33)^{2}}{44.33}$ + $\frac{(40-47.67)^{2}}{47.67}$ + $\frac{(47-47.67)^{2}}{47.67}$ + $\frac{(56-47.67)^{2}}{47.67}$
=1.326+0.010+1.566+1.233+0.009+1.457
=5.602
Step 4:
Since 5.602 < 9.210 , the decision is to not reject the null hypothesis.
Step 5:
There is not enough evidence to claim that the malls and the proportions of customers who are willing to participate in a marketing research survey are dependent upon each other.
