A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population):
x1: New England crime rate

Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population):
x2: Rocky Mountain states crime rate

Assume that the crime rate distribution is approximately normal in both regions. Use a calculator to verify that 1 ‰ˆ 3.51, s1 ‰ˆ 0.81, 2 ‰ˆ 3.87, and s2 ‰ˆ 0.94.
(a) Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than that in New England? Use α = 0.01.
(b) Find a 98% confidence interval for μ1 - μ2. Explain the meaning of the confidence interval in the context of the problem.
Please provide the following information for problem part (a):
(i) What is the level of significance? State the null and alternate hypotheses.
(ii) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(iii) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(iv) Based on your answers in parts (i) €“ (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(v) Interpret your conclusion in the context of the application.

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