Question

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 μ₁ − μ₂. Round the test statistic and critical value to three decimal places.)

test statistic
critical value

Answer 1

	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