Question

From a random sample of 22 cities of various sizes, data is collected from police records regarding violations of the narcotic drug laws per 100,000 inhabitants. The communities were broken down into 4 sizes (large cities, small cities, suburban communities, and rural communities), and data was collected over the period of one calendar year. Please determine if there is significant evidence to conclude that the mean rates of arrests for narcotics is different in each community (based on their size). Please conduct this test at the 99% confidence level.

City Community
Large: 45, 34, 41, 42, 37 Suburban: 25, 17, 19, 28, 31, 37
Small: 23, 24, 27, 21, 26, 34 Rural: 13, 16, 14, 17, 10

Answer 1

Answer on Question #60867 – Math – Statistics and Probability

Question

From a random sample of 22 cities of various sizes, data is collected from police records regarding violations of the narcotic drug laws per 100,000 inhabitants. The communities were broken down into 4 sizes (large cities, small cities, suburban communities, and rural communities), and data was collected over the period of one calendar year. Please determine if there is significant evidence to conclude that the mean rates of arrests for narcotics is different in each community (based on their size). Please conduct this test at the 99% confidence level.

City Community

Large: 45, 34, 41, 42, 37 Suburban: 25, 17, 19, 28, 31, 37

Small: 23, 24, 27, 21, 26, 34 Rural: 13, 16, 14, 17, 10

Solution

Null hypothesis $H_0$: all means are equal;

Alternative hypothesis $H_a$: not all means are equal.

Using Data Analysis Tool 'Anova: Single Factor' from Microsoft Excel obtain the following output:

SUMMARY

ANOVA

As we can see the P-value for Between groups equals $4.92 * 10^{-6}$. Therefore, there is significant evidence to conclude that the mean rates of arrests for narcotics is different in each community.

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