Answer
Step 1:
$H_0$ : The proportions of the degree recipients received different types of degrees are as follows: 23.3% associate degrees, 51.1% bachelor degrees, 3% first professional degrees, 20.6% master degrees, and 2% doctorates.
$H_1$: The distribution is not the same as stated in the null hypothesis.
Step 2:
Since α=0.05, and the degrees of freedom are 5-1=4 , the critical value is 13.277.
Step 3:
Expected Value:
0.233 * 800 = 186.4
0.511 * 800 = 408.8
0.03 * 800 =24
0.206 * 800 =164.8
0.02 * 800 =16
Test Value :
χ2 = Σ $\frac{(O-E)^{2}}{E}$ =$\frac{(155-186.4)^{2}}{186.40}$ + $\frac{(155-186.4)^{2}}{186.4}$ + $\frac{(450-408.8)^{2}}{408.8}$ + $\frac{(20-24)^{2}}{24}$ + $\frac{(160-164.8)^{2}}{164.8}$ + $\frac{(15-16)^{2}}{16}$ +
=5.289
=10.311
Step 4:
Since 10.331< 13.277, 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 do not differ from the report.
