Answer
$X^2\gt X_α^2$: the null hypothesis is rejected. Thus there is significant evidence that the first digits of the checks do not obey Benford's Law.
Work Step by Step
$H_0:~the~digits~obey~Benford’s~Law$
$H_1:~the~digits~do~not~obey~Benford’s~Law$
Total frequency: $36+32+28+26+23+17+15+16+7=200$
Expected count of 1: $200\times0.301=60.2$
Expected count of 2: $200\times0.176=35.2$
Expected count of 3: $200\times0.125=25$
Expected count of 4: $200\times0.097=19.4$
Expected count of 5: $200\times0.079=15.8$
Expected count of 6: $200\times0.067=13.4$
Expected count of 7: $200\times0.058=11.6$
Expected count of 8: $200\times0.051=10.2$
Expected count of 9: $200\times0.046=9.2$
$X^2=Σ\frac{(O_i-E_i)^2}{E_1}=\frac{(36-60.2)^2}{60.2}+\frac{(32-35.2)^2}{35.2}+\frac{(28-25)^2}{25}+\frac{(26-19.4)^2}{19.4}+\frac{(23-15.8)^2}{15.8}+\frac{(17-13.4)^2}{13.4}+\frac{(15-11.6)^2}{11.6}+\frac{(16-10.2)^2}{10.2}+\frac{(7-9.2)^2}{9.2}=21.693$
$k=9$. So, $d.f.=9-1=8$
$X_α^2=X_{0.01}^2=20.090$
(According to Table VII, for d.f. = 8 and area to the right of critical value = 0.01)
Since $X^2\gt X_α^2$, we reject the null hypothesis.
