A researcher wants to know if the violent crime rate is the same in the New England states as in the Rocky Mountain states. A random sample of n1 =8 regions in New England had a mean violent crime rate of

¯
1
=4.9
X
¯
1
=
4.9
 (per million population).
The standard deviation in this area is σ1 = 1.1.
A random sample of n2 = 14 regions in the Rocky Mountain states had a mean violent crime rate of

¯
2
=3.7
X
¯
2
=
3.7
 (per million population).
The standard deviation in this area is σ2 = 0.4.
At α = 0.05, test the claim that the average violent crime rate in New England is the same as in the Rocky Mountains.