Answer
See below.
Work Step by Step
The null hypothesis says that the population proportions are equal to each other and thus equal to one divided by the number of categories:
$H_0:p_1=p_2=p_3=p_4=p_5=p_6=p_7=\frac{1}{7}\approx0.1429$
The alternative hypothesis says the opposite of the null hypothesis, which is that at least one of the proportions doesn't equal all the others.
The expected frequencies are $E_i=n\cdot p_i$.
