Bonferroni interval - quick example calculation

Question

Problem statement:

Calculate the Bonferroni interval for any pair of means $\bar{y}_{.j},\bar{y}_{.k}$ with $I$=10 groups with equal sample size 30 in each group. Write this as a multiple of $s$.

Attempt at solution:

The Bonferroni interval is:

$$ \bar{y}_{.j} - \bar{y}_{.k} \pm t_{1 - \frac{0.05}{2 \left(\begin{array}{c} 10\\2 \end{array} \right)}, n - J} s\sqrt{\frac{1}{30} + \frac{1}{30}} $$

Which simplifies to

$$ \bar{y}_{.j} - \bar{y}_{.k} \pm t_{1 - \frac{0.05}{90}, n - J} s\sqrt{\frac{1}{15}}. $$

According to the notes the solution is:

$$ \bar{y}_{.j} - \bar{y}_{.k} \pm s(0.7969) $$

But I am unable to generate the correct solution. I suspect my choice of $n$ and $J$ are the culprits. I thought they were 60 - 2 but when I plug this into R I get:

qt(1-(0.05/90), 58) * sqrt(1/15)
[1] 0.8861344

Answer 1

There are 45 pairs, not 90 pairs. You can count like 1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8 1-9 1-10, 2-3 2-4....

The sample standard deviation will come from 300 subjects, but there are 10 sample means, so degree of freedom should be 290.

So this is what I got:

    qt(1-(0.05/45), 290) * sqrt(1/15)
    [1] 0.796889