Answer
$X^2_0\lt X_α^2$: null hypothesis is not rejected.
There is not enough evidence to conclude that the distribution of educational attainment has changed since 2000.
Work Step by Step
$H_0:$ the distribution of educational attainment has not changed since 2000
versus
$H_1:$ the distribution of educational attainment has changed since 2000
In MINITAB, enter the observed values in C1 and the relative frequencies in C2.
Select Stat -> Tables -> Chi-square Goodness-of-Fit Test (One Variable)
Select Observed counts and enter C1. Select specific proportions and enter C2.
Click OK.
$X^2_0=2.66083$
$k=6$.
So, $d.f.=6-1=5$
$X_α^2=X_{0.1}^2=9.236$
(According to Table VII, for d.f. = 5 and area to the right of critical value = 0.1)
Since $X^2_0\lt X_α^2$, we do not reject the null hypothesis.
Also, P-value $=0.752\gtα$
