Problem $9$ The density of Polyethylene can be used as a measure of its molecular structure: Mostly straight chains pack more closely and therefore have a higher density than branched chains. Differences in density can cause processing problems like poor bending and inaccurate compositions. The mean density of $80$ PE pellets measured on the morning shift was $950+20$ kg$/$m$^3$ and the mean density of $65$ PE pellets measured on the evening shift was $940+15$ kg$/$m$^3.$ Are the two means different?