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 3.4 3.6 4.0 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 3.8 4.5 4.4 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. (i) Use a calculator to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (ii) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use α = 0.05.

(a) What is the level of significance? State the null and alternate hypotheses. H0: μ1 < μ2; H1: μ1 = μ2 H0: μ1 = μ2; H1: μ1 < μ2 H0: μ1 = μ2; H1: μ1 > μ2 H0: μ1 = μ2; H1: μ1 ≠ μ2

(b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. What is the value of the sample test statistic? (Test the difference μ1 − μ2. Round your answer to three decimal places.)

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Answer 1

N1 = 10 N2 = 12

X1 = 3.51

S1 = 0.8252 = 0.83

X2 = 3.90

S2=0.9752=0.98

a) H0: μ1 = μ2;

H1: μ1 < μ2

The standard normal. We assume that both population distributions are approximately normal with known standard deviations. .