Question

Part 1) The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.

Age (years)	Percent of Canadian Population	Observed Number in the Village
Under 5	7.2%	46
5 to 14	13.6%	76
15 to 64	67.1%	288
65 and older	12.1%	45

a) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)

b) What are the degrees of freedom?

c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.)

Part 2) The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site.

Raw Material	Regional Percent of Stone Tools	Observed Number of Tools as Current excavation Site
Basalt	61.3%	889
Obsidian	10.6%	164
Welded Tuff	11.4%	169
Pedemal chert	13.1%	203
Other	3.6%	61

a) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)
b) What are the degrees of freedom?

c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

Answer 1

Part I) ### By using Excel

Age	Proportion(Pi)	Observed(O)	Expected(E)=n*Pi	O-E	(O-E)^2	(O-E)^2/E
Under 5	0.072	46	32.76	13.24	175.2976	5.350965
5 to 14	0.136	76	61.88	14.12	199.3744	3.221952
15 to 64	0.671	288	305.305	-17.305	299.463	0.980865
65 and older	0.121	45	55.055	-10.055	101.103	1.8364
	n=	455			Sum=	11.39018

a) the chi-square statistic for the sample is given by

b) Here the degrees of freedom =3

c) The pvalue is : 0.0098 ### By using Excel command: =(CHIDIST(11.39,3))

PartII)### Using Excel

Raw Material	Proportion(Pi)	Observed(O)	Expected(E)=n*Pi	O-E	(O-E)^2	(O-E)^2/E
Basalt	0.613	889	910.918	-21.918	480.3987	0.527379
Obsidian	0.106	164	157.516	6.484	42.04226	0.266908
Welded tuff	0.114	169	169.404	-0.404	0.163216	0.000963
pedemal chert	0.131	203	194.666	8.334	69.45556	0.356793
Other	0.036	61	53.496	7.504	56.31002	1.052602
	n=	1486			Sum=	2.204646

a)

b) Here degrees of freedom are: 4

c) The Pvalue is 0.698 ### By using Excel command: =(CHIDIST(2.205,4))