A researcher interested in aggression identified the 10 hottest and coldest U.S.

Question

A researcher interested in aggression identified the 10 hottest and coldest U.S. cities and assessed murder rates in each city. The hypothesis was that because heat facilitates aggression, the hottest cities would have higher murder rates than the coldest cities. Each city name below is followed by the number of murders per 100,000 people committed in that city in 2006. Conduct the appropriate statistical test to determine if there is support for the researcher’s hypothesis.

Murder Murder Rate Hot Cities Rate Cold Cities 1. International Falls 19.6 2. Duluth, Minnesota 17 3. Caribou, Maine 25.2 4. Marquette, Michigar 1. Key West, Florida 0.0 Minnesota 2. Miami, Florida . W. Palm Beach, Florida 4. Ft. Myers, Florida 5. Yuma, Arizona 6. Brownsville, Texas 7. Orlando, Florida 8. Vero Beach, Florida 9. Corpus Christi, Texas 10. Tampa, Florida Note: Murder rate data were taken from http:/fargond.areaconnect.com/crime/compare 1.2 0.0 0.0 0.0 2.2 0.0 0.0 3.4 2.9 22.6 5. Sault Ste Marie, Michigan 6. Fargo, North Dakota 7. Williston, North Dakota 0.0 8. Alamosa, Colorado .2 9. Bismarck, North Dakota 7.5 10. St. Cloud, Minnesota 0.0 htm. The hottest and coldest U.S. city list can be found at http://web2.airmail.net/danbl/ usrecords.htm

Explanation / Answer

Two-sample T for hot vs cold

       N   Mean StDev SE Mean
hot   10 10.96   9.23      2.9
cold 10 0.510 0.854     0.27

Difference = (hot) - (cold)
Estimate for difference: 10.45
95% CI for difference: (4.29, 16.61)
T-Test of difference = 0 (vs ): T-Value = 3.57 P-Value = 0.002 DF = 18
Both use Pooled StDev = 6.5515

since p-value = 0.002 < 0.01

we reject the null and conclude that there is significant evidence that the hottest cities have higher murder rates than the coldest cities.

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