# CHI SQUARE TEST

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The Facts:

Each year, the National Highway Traffic Safety Administration (NHTSA) with the National Center for Statistics and Analysis (NCSA) publishes Traffic Safety Facts, which summarizes the motor vehicle traffic crashes for the United States. Traffic Safety Facts 2005 includes trend data, crash data, vehicle data, and people data. Also, the NHTSA and NCSA publish a report summarizing the motor vehicle crash data of the 32 states in the NHTSA's State Data System.

In 2005 there were 43,443 fatalities in the United States as a result of motor vehicle crashes. The pie chart at the right shows the national distribution of traffic fatalities with respect to age group. For example, 16% of all motor vehicle fatalities were adults age 25-34. Using the data from the 32 states in the NHTSA's State Data System as a sample, the contingency table shows the number of motor vehicle fatalities according to the age and geographic location within the United States.

Age Eastern US Central US Western US

Under 16 651 841 414

16-24 3309 3478 1655

25-34 2255 2346 1154

35-44 2132 2163 1021

45-54 1977 1994 955

55-64 1359 1361 668

65-74 941 939 386

75+ 1354 1190 498

1. At alpha=0.05, perform a chi-square independence test to determine whether the variables region and age are independent. What can you conclude?

2. Compare the distribution of the sample of motor vehicle fatalities from the eastern United States with the National distribution. What can you conclude?

3. Compare the distribution of the sample of motor vehicle fatalities from the United States with the national distribution. What can you conclude?

4. Compare the distribution of the sample of motor vehicle fatalities from the western United States with the national distribution. What can you conclude?

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##### Solution Summary

Two popular chi square tests, chi square test of independence of qualitative characteristics, and chi square test of goodness of fit were done on the problem given. The general procedure of these two tests is first discussed and then the problem is worked out.

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