Answer
Step 1:
$H_0$ : The sales of CDs(in thousands) by genre and the year in which the sales occurred are independent from each other.
$H_1$: The sales of CDs(in thousands) by genre and the year in which the sales occurred are dependent upon each other.
Step 2:
Since α=0.05, the critical value using Table G with (2-1)(3-1) = (1)(3) =3 degrees of freedom is 7.815.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(55863)(34561)}{(120.710)}$ = 15994.38
$E_1,2$ = $\frac{(55863)(35933)}{(120.710)}$ = 16629.32
$E_1,3$ = $\frac{(55863)(50216)}{(120.710)}$= 23239.30
$E_2,$ = $\frac{(64847)(34561)}{(120.710)}$ = 18566.62
$E_2,2$ = $\frac{(64847)(35933)}{(120.710)}$ = 19303.68
$E_2,3$ = $\frac{(64847)(50216)}{(120.710)}$ = 26976.70
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(15875-15994.38)^{2}}{15994.38}$ + $\frac{(17139-16629.32)^{2}}{16629.32}$ + $\frac{(22849-23239.3)^{2}}{23239.3}$ + $\frac{(18686-18566.62)^{2}}{18566.62}$ + $\frac{(18794-19303.68)^{2}}{19303.68}$ + $\frac{(27367-26976.7)^{2}}{26976.7}$
=0.891+15.621+6.555+0.788+13.457+5.647
=42.939
Step 4:
Since 42.939 > 7.815, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that the sales of CDs (in thousands) by genre and the year in which the sales occurred are dependent upon each other.
