Answer
8.
Step 1:
$H_0$ :Movie admissions are independent from ethnicity
$H_1$: Movie admissions are dependent upon ethnicity.
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:
$E_1,1$ = $\frac{(1472)(1845)}{(2943)}$ = 922.81
$E_1,2$ = $\frac{(1472)(537)}{(2943)}$ = 268.59
$E_1,3$ = $\frac{(1472)(345)}{(2943)}$= 172.56
$E_1,4$ = $\frac{(1472)(216)}{(2943)}$ = 108.04
$E_2,1$ = $\frac{(1471)(1845)}{(2943)}$ = 922.19
$E_2,2$ = $\frac{(1471)(537)}{(2943)}$ = 268.41
$E_2,3$ = $\frac{(1471)(345)}{(2943)}$ = 172.44
$E_2,4$ = $\frac{(1471)(216)}{(2943)}$ = 107.96
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(936-922.81)^{2}}{922.81}$ + $\frac{(240-268.59)^{2}}{268.59}$ + $\frac{(195-172.56)^{2}}{172.56}$ + $\frac{(101-108.04)^{2}}{108.04}$ + $\frac{(909-922.19)^{2}}{922.19}$ + $\frac{(297-268.41)^{2}}{268.41}$ + $\frac{(150-172.44)^{2}}{172.44}$ + $\frac{(115-107.96)^{2}}{107.96}$ +
=0.188+3.044+2.919+0.458+0.189+3.046+2.921+0.459
=13.222
Step 4:
Since 13.222 > 7.815, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that the movie admissions are dependent upon ethnicity.
