Answer
Step 1:
$H_0$ : The cities are independent from the type of crime committed.
$H_1$: The cities are dependent upon the type of crime committed.
Step 2:
Since α=0.05, the critical value using Table G with (4-1)(3-1) = (3)(2) =6 degrees of freedom is 13.592.
Step 3:
Expected Value:
$E_1,1$ = $\frac{(119)(85)}{(502)}$ = 20.15
$E_1,2$ = $\frac{(119)(1410)}{(502)}$ = 33.42
$E_1,3$ = $\frac{(119)(276)}{(502)}$= 65.43
$E_1,4$ = $\frac{(119)(85)}{(502)}$= 20.15
$E_2,1$ = $\frac{(119)(141)}{(502)}$ = 33.42
$E_2,2$ = $\frac{(119)(276)}{(502)}$ = 65.43
$E_2,3$ = $\frac{(128)(85)}{(502)}$ = 21.67
$E_2,4$ = $\frac{(128)(141)}{(502)}$ = 35.95
$E_3,1$ = $\frac{(128)(276)}{(502)}$ = 70.37
$E_3,2$ = $\frac{(136)(85)}{(502)}$ = 23.03
$E_3,3$ = $\frac{(136)(141)}{(502)}$ = 38.20
$E_3,4$ = $\frac{(136)(276)}{(502)}$ = 74.77
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$
=
$\frac{(14-20.15)^{2}}{20.15}$ + $\frac{(35-33.42)^{2}}{33.42}$ + $\frac{(70-65.43)^{2}}{65.43}$ + $\frac{(10-20.15)^{2}}{20.15}$ + $\frac{(33-33.42)^{2}}{33.42}$ + $\frac{(76-65.43)^{2}}{65.43}$ + $\frac{(14-21.67)^{2}}{21.67}$ + $\frac{(37-35.95)^{2}}{35.95}$ + $\frac{(77-70.37)^{2}}{70.37}$ +$\frac{(47-23.03)^{2}}{23.03}$ + $\frac{(36-38.20)^{2}}{38.20}$ + $\frac{(53-74.77)^{2}}{74.77}$
=1.877+0.074+0.320+5.112+0.005+1.709+2.717+0.031+0.624+24.955+0.127+6.340
=43.890
Step 4:
Since 43.890 > 13.592, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to claim that the cities are dependent upon the type of crime committed.
