A gelato shop tries to give consistent scoop sizes, but some flavors of gelato are denser than others. Here's the historical data for the mass per scoop of two flavors:
Flavor
Shape
Mean (g)
Standard deviation (g)
Hazelnut
Normal
83
9.3
Dulce de leche
Normal
67.5
7.8
Suppose they weigh a sample of 20 randomly selected scoops of hazelnut gelato and 15 scoops of dulce de
leche gelato. They will then look at the difference in their sample means (Tu – īp).
What do we know about the shape of the sampling distribution of CH
TD, and why?