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 3.5 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 3.9 4.3 4.5 5.1 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.

(i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to three decimal places.)

x1 =

s1 =

x2 =

s2 =

Does the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use α = 0.01.

(a) What is the level of significance?

(b) What is the value of the sample test statistic? (Test the difference μ₁ − μ₂. Round your answer to three decimal places.)

Answer 1

Let denote the mean violent crime rate in New England and in the Rocky Mountain region respectively.