Answer
Step 1:
$H_0$ : The proportions of the each type of car purchased are as follows: Luxury 15.6%, large 6%, midsize 42%, small 36.4%.
$H_1$: The distribution is not the same as stated in the null hypothesis.
Step 2:
Since α=0.10, and the degrees of freedom are 4-1=3 , the critical value is 6.251.
Step 3:
Expected Value:
0.156 * 150 = 23.4
0.06 * 150 = 9
0.42 * 150 =63
0.364 * 150 =54.6
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$ =$\frac{(25-23.4
)^{2}}{23.4}$ + $\frac{(12-9)^{2}}{9}$ + $\frac{(60-63)^{2}}{63}$+ $\frac{(53-454.6)^{2}}{54.6}$ =0.109+1+0.143+0.047=1.299
Step 4:
Since 1.299 < 6.251, the decision is not to reject the null hypothesis.
Step 5:
There is no enough evidence to reject the claim and hence we conclude that the proportions of each type of car purchased is not differed from the report.
