Answer
Step 1:
$H_0$ : The proportions of the most popular colors for light trucks are as follows: 30% white, 17% black, 14% red, 12% silver, 11% gray, 8% blue, 6% others.
$H_1$: The distribution is not the same as stated in the null hypothesis.
Step 2:
Since α=0.05, and the degrees of freedom are 7-1=6 , the critical value is 12.592
Step 3:
Expected Value:
0.3 * 180 = 54
0.17 * 180= 30.6
0.14 * 180 = 25.2
0.12 *180 = 21.6
0.11 *180 = 19.8
0.08 *180 = 14.4
0.06 *180 = 10.8
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$ =$\frac{(45-54)^{2}}{54}$ + $\frac{(32-30.6)^{2}}{30.6}$ + $\frac{(30-25.2)^{2}}{25.2}$+ $\frac{(30-21.6)^{2}}{21.6}$+ $\frac{(22-19.8)^{2}}{19.8}$+ $\frac{(15-14.4)^{2}}{14.4}$+ $\frac{(6-10.8^{2}}{10.8}$
=1.5+0.064+0.914+3.267+0.244+0.025+2.133
=8.148
Step 4:
Since 8.148 < 12.592, the decision is not to reject the null hypothesis.
Step 5:
There is no enough evidence to reject the claim , hence we conclude that the proportions are not differ from those stated.
