3. A machine fills bottles with 64 fluid ounces of Slurm, a popular and highly addictive

soft drink. The quality-control manager determines that the fill levels are normally

distributed with a mean of 64 ounces and a standard deviation of 0.42 ounce. He has

an engineer recalibrate the machine in an attempt to lower the standard deviation.

After recalibration, the quality-control manager randomly selects 19 bottles from the

line and determines that the standard deviation is 0.38 ounce. Is there less variability

in the filling machine? Use the α = 0.01 level of significance.