Question

A researcher claims that the number of homicide crimes by season is uniformly distributed. To test this​ claim, you randomly select 1 comma 1921,192 homicides from a recent year and record the season when each happened. The table shows the results. At alphaα ​= 0.100.10​, test the​ researcher's claim.		Season	​Frequency, f
		Spring	301301
		Summer	315315
		Fall	296296
		Winter	280280

State

Upper H 0H0

and

Upper H Subscript aHa

and identify the claim.

Upper H 0H0​:

The distribution of the number of homicide crimes by season

is uniformly distributed.

Upper H Subscript aHa​:

The distribution of the number of homicide crimes by season

is not uniformly distributed.

Which hypothesis is the​ claim?

Upper H 0H0

Your answer is correct.

Upper H Subscript aHa

Calculate the test statistic.

Answer 1

Ho:The distribution of the number of homicide crimes by season is uniformly distributed.

Ha: The distribution of the number of homicide crimes by season is not uniformly distributed.

Ho is the claim:

Applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Spring	0.250	301	298.00	0.17	0.030
summer	0.250	315	298.00	0.98	0.970
Fall	0.250	296	298.00	-0.12	0.013
Winter	0.250	280	298.00	-1.04	1.087
total	1.000	1192	1192		2.101

test statistic =2.101

(crtical value =6.251 ; p value =0.5518 ; fail to reject Ho)