Answer
$H_0$ : The proportions of the customers in the three stores who made a list before going shopping and the stores are independent from each other.
$H_1$: The proportions of the customers in the three stores who made a list before going shopping and the stores are dependent upon each other.
Step 2:
Since α=0.1, the critical value using Table G with (2-1)(3-1) = (1)(2) =2 degrees of freedom is 4.605.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(219)(96)}{(288)}$ = 73
$E_1,2$ = $\frac{(219)(96)}{(288)}$ = 73
$E_1,3$ = $\frac{(219)(96)}{(288)}$= 73
$E_2,1$ = $\frac{(69)(96)}{(288)}$ = 23
$E_2,2$ = $\frac{(69)(96)}{(288)}$ = 23
$E_2,3$ = $\frac{(69)(96)}{(288)}$ = 23
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(77-73)^{2}}{73}$ + $\frac{(74-73)^{2}}{73}$ + $\frac{(68-73)^{2}}{73}$ + $\frac{(19-23)^{2}}{23}$ + $\frac{(22-23)^{2}}{23}$ + $\frac{(28-23)^{2}}{23}$
=0.219+0.014+0.342+0.696+0.043+1.087
=2.401
Step 4:
Since 2.401 < 4.605, the decision is to reject the null hypothesis.
Step 5:
There is not enough evidence to claim that the proportions of the customers in the three stores who made a list before going shopping and the stores are dependent upon each other.
