Question

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

550 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	0.012	5
Forcible Rape	0.074	33
Robbery	0.360	201
Aggravated Assault	0.554	311

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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.

Part 1 of 4

Your Answer is correct

(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.

Part: 1 / 4

1 of 4 Parts Complete

Part 2 of 4

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

The P -value is .

Answer 1

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.

Part 2 of 4

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.012	5	6.60	-0.62	0.388
2	0.074	33	40.70	-1.21	1.457
3	0.360	201	198.00	0.21	0.045
4	0.554	311	304.70	0.36	0.130
total	1.000	550	550		2.0203
test statistic X2 =		2.020

degree of freedom =categories-1=

3

p value =

0.5682 (form excel function chidist(2.020,3)