Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-The manager of a juice bottling factory is considering installing a new juice bottling machine which she hopes
will reduce the amount of variation in the volumes of juice dispensed into 8-fluid-ounce bottles. Random
samples of 10 bottles filled by the old machine and 9 bottles filled by the new machine yielded the following
volumes of juice (in fluid ounces). Old machine: $\quad 8.2,8.0,7.9,7.9,8.5,7.9,8.1,8.1,8.2,7.9$
New machine: $8.0,8.1,8.0,8.1,7.9,8.0,7.9,8.0,8.1$ Use a 0.05 significance level to test the claim that the volumes of juice filled by the old machine vary more than
the volumes of juice filled by the new machine. $$\left( \text { Note } : \mathrm { s } _ { 1 } = 0.1947 \mathrm { fl } \mathrm { oz } , \mathrm { s } _ { 2 } = 0.0782 \mathrm { fl } \mathrm { oz } \right)$$