Answer
$0.22\leq \sigma \leq 0.44$
Work Step by Step
We are given $n=18, s=0.29, c=0.95$
use the $\chi^2$ table with $df=17$ and $\alpha/2=0.025, 0.975$
we found $\chi^2_{left}=7.564$ and $\chi^2_{right}=30.191$
The confidence interval is given by: $s\times\sqrt {\frac{n-1}{\chi^2_{right}}}$ to $s\times\sqrt {\frac{n-1}{\chi^2_{left}}}$
which gives: $0.29\times\sqrt {\frac{17}{30.191}}=0.218$ to $0.29\times\sqrt {\frac{17}{7.564}}=0.435$
The 95% confidence interval of the true
standard deviation of the diameters of the baseballs is $0.22\leq \sigma \leq 0.44$
