Question

# A random sample of n1 = 10 regions in New England gave the following violent crime...

A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population).

x1:      New England Crime Rate

 3.3 3.7 4.2 4.1 3.3 4.1 1.8 4.8 2.9 3.1

Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population).

x2:      Rocky Mountain Crime Rate

 3.5 4.3 4.5 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8

Assume that the crime rate distribution is approximately normal in both regions. Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use α = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference μ1μ2. Round the test statistic and critical value to three decimal places.)

 test statistic critical value

 New England Rocky Mountain x1    = 3.530 x2      = 3.867 s1    = 0.845 s2      = 0.977 n1    = 10 n2     = 12
 degree of freedom v ='min(n1,n2)-1= 9
 std error =√(S21/n1+S22/n2)= 0.3885 test statistics t =(x1-x2-Δo)/Se = -0.867
 for 0.01 level ,left tail test &9 df, critical t= -2.821