Answer
Step 1:
$H_0$ : The types of meal purchased are independent of the restaurant.
$H_1$: The types of meal purchased are dependent on the restaurant.
Step 2:
Since α=0.01, the critical value using Table G with (3-1)(3-1) = (2)(2) =4 degrees of freedom is 13.277.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(98)(100)}{(300)}$ = 32.67
$E_1,2$ = $\frac{(98)(100)}{(300)}$ = 32.67
$E_1,3$ = $\frac{(98)(100)}{(300)}$= 32.67
$E_2,1$ = $\frac{(113)(100)}{(300)}$ = 37.67
$E_2,2$ = $\frac{(113)(100)}{(300)}$ = 37.67
$E_2,3$ = $\frac{(113)(100)}{(300)}$ = 37.67
$E_3,1$ = $\frac{(89)(100)}{(300)}$ = 29.67
$E_3,2$ = $\frac{(89)(100)}{(300)}$ = 29.67
$E_3,3$ = $\frac{(89)(100)}{(300)}$ = 29.67
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(26-32.67)^{2}}{32.67}$ + $\frac{(29-32.67)^{2}}{32.67}$ + $\frac{(43-32.67)^{2}}{32.67}$ + $\frac{(53-37.67)^{2}}{37.67}$ + $\frac{(27-37.67)^{2}}{37.67}$ + $\frac{(33-37.67)^{2}}{37.67}$ + $\frac{(21-29.67)^{2}}{29.67}$ + $\frac{(44-29.67)^{2}}{29.67}$ + $\frac{(24-29.67)^{2}}{29.67}$
=1.361+0.412+3.269+6.242+3.021+0.578+2.532+6.925+1.082
=25.421
Step 4:
Since 25.421 > 13.277, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that the types of meal purchased by the patrons are dependent upon the restaurant.
