Answer
Step 1:
$H_0$ : The proportions of the people pay for their medical prescription is as follows: 60% personal funds, 25% insurance, 15% Medicare.
$H_1$: The distribution is not the same as stated in the null hypothesis.
Step 2:
Since α=0.05, and the degrees of freedom are 3-1=2 , the critical value is 5.991.
Step 3:
Expected Value:
0.6 * 50 = 30
0.25 * 50 = 12.50
0.15 * 50 =7.50
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$ =$\frac{(32-30
)^{2}}{30}$ + $\frac{(10-12.50)^{2}}{12.50}$ + $\frac{(8-7.50)^{2}}{7.50}$ =0.133+0.5+0.033=0.667
Step 4:
Using P-value method,
Since P(Χ2 > 0.667) = 0.43 > α , the decision is to not 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 has no difference from the null hypothesis.
