The felonies committed in a certain county are classified into the following gen

Question

The felonies committed in a certain county are classified into the following general categories: violent crimes (murder, assault, etc), theft (including burglary and larceny), fraud (including tax evasion), and possession/sale of illegal substances. The distribution of such crimes in 1990 was as follows: Violenceft F Fraud Ilegal Substances .30 18 36 16 For the year 2016, there were 800 felonies committed in the county according to county records. The following is the total for each category: Violence Theft Fraud Illegal Substances 280 300 120 100 Test whether the distribution of crimes has changed significantly since 1990 at = .05. If there is a significant difference, describe which categories are most responsible for the difference.

Explanation / Answer

H0: The distribution of crimes has not changed significantly

H1: The distribution of crimes has changed significantly

Let the los be alpha = 5%

The chisquare contribution values are calculated as follows

Test Statistic, X^2: 21.1111

Num Categories: 4
Degrees of freedom: 3

Critical X^2: 7.814736
P-Value: 0.0001

Here Chisquare value > chsiquare critical value, and p-value < alpha 0.05, so we reject H0

Thus we conclude that the distribution of crimes has changed significantly

Observed Expected Freq (Oi) Prob Freq Ei (Oi-Ei)^2 /Ei 100 0.18 144 13.44444444 300 0.36 288 0.5 120 0.16 128 0.5 280 0.3 240 6.666666667 Total: 800 1 800 21.11111111

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