Question

A researcher wants to know if the violent crime rate is the same in the New England states as in the Rocky Mountain states. A random sample of n1 = 8 regions in New England had a mean violent crime rate of ¯1 = 4.9 (per million population). The standard deviation in this area is σ1 = 1.1. A random sample of n2 = 14 regions in the Rocky Mountain states had a mean violent crime rate of ¯2 = 3.7 (per million population). The standard deviation in this area is σ2 = 0.4. At α = 0.05, test the claim that the average violent crime rate in New England is the same as in the Rocky Mountains.

A) Accept the null hypothesis
B) Reject the null hypothesis
C) Insufficient information to decide
D) The researcher should conduct a larger sample

Answer 1

The question involves hypothesis testing with a two-sample t-test to compare average violent crime rates between New England and Rocky Mountain states, given the data and α = 0.05 to determine if we reject or do not reject the null hypothesis.

Step-by-step explanation:

The student's question is focused on determining if the average violent crime rate in New England is the same as in the Rocky Mountain states using hypothesis testing. Given the sample sizes, means, standard deviations, and the significance level (α = 0.05), we can perform a two-sample t-test.

The null hypothesis (H0) for this study would be H0: μ1 - μ2 = 0, which states that there is no difference in the violent crime rates between the two regions. The alternative hypothesis (Ha) is Ha: μ1 - μ2 ≠ 0, which suggests that there is a difference.

To test this hypothesis, we would calculate the test statistic using the provided means, standard deviations, and sample sizes, and then compare the result to the t-distribution to determine the p-value.

If the p-value is less than the significance level of 0.05, we reject the null hypothesis; otherwise, we do not reject it.