A governmental agency computed the proportion of violent crimes in the United States in a particular year falling into each of four categories. A simple random sample of

580

violent crimes committed in California during that year were categorized in the same way. The following table presents the results.

Category	U.S. Proportion	California Frequency
Murder	0.015	5
Forcible Rape	0.055	31
Robbery	0.380	208
Aggravated Assault	0.550	336

Can you conclude that the proportions of crimes in the various categories in California differ from those in the United States as a whole? Use the 0.05 level of significance and the P-value method with the TI-

84

Plus calculator.

(a) State the null and alternate hypotheses.

H0: The proportions of crimes in the various categories in California are the same as those in the United States as a whole.

H1

: The proportions of crimes in the various categories in California are not the same as those in the United States as a whole.

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(b) Find the P-value. Round the answer to at least four decimal places.

C. What are the critical values of a = 0.05

D. Do we reject Ho ?

E. Do we have enough evidence to support the hypothesis?