Answer
Step 1:
$H_0$ : The proportions of college students and their recent purchases are as follows: 77.8% were full-lengths CDs, 12.8% were digital downloads, 3.8% were singles, others were 5.6%.
$H_1$: The distribution is not the same as stated in the null hypothesis.
Step 2:
Since α=0.05, and the degrees of freedom are 4-1=3 , the critical value is 7.815.
Step 3:
Expected Value:
0.778 * 200 = 155.6
0.128 * 200 = 25.6
0.038 * 200 = 7.6
0.056 *200 = 11.2
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$ =$\frac{(135-155.6)^{2}}{155.6}$ + $\frac{(48-25.6)^{2}}{25.6}$ + $\frac{(10-7.6)^{2}}{7.6}$ + $\frac{(7-11.2)^{2}}{11.2}$
=2.727+19.6+0.758+1.575
=24.660
Step 4:
Since 24.660 > 7.815, the decision is to reject the null hypothesis.
Step 5:
There is enough evidence to reject the claim and conclude that at least one of the proportions differs from its original value.
