Answer
$76.9\leq \mu\leq 88.3$
Work Step by Step
From the data set we have $n=11, \bar X=82.6, s=8.5$
With $df=n-1=10, \alpha/2=0.025$ we can find $t_{\alpha/2}=2.228$
The margin of error $E=t_{\alpha/2}\times\frac{s}{\sqrt n}=2.228\times\frac{8.5}{\sqrt 11}=5.7$
The confidence interval is $(82.6-5.7, 82.6+5.7)$ which is $(76.9, 88.3)$
So the true mean length of all children’s animated films with 95% confidence is $76.9\leq \mu\leq 88.3$
