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 3.0 3.1 4.0 3.9 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 4.1 4.8 5.3 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. Note: If a two-sample t-test is appropriate, for degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer.

Use a calculator to calculate x1=, s1=, x2= , and s2=. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (a) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use α = 0.01. (i)

What is the level of significance?

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


(iii) Find the P-value. (Round your answer to four decimal places.)

) Find a 98% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

lower limit
upper limit

Answer 1