Question

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%	49
5 to 14	13.6%	76
15 to 64	67.1%	283
65 and older	12.1%	47

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

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

c) What are the degrees of freedom?

d) (c) Estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100    

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

Answer 1

b)

applying chi square goodness if fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
under 5	0.072	49	32.76	2.84	8.051
5 to 14	0.136	76	61.88	1.79	3.222
15-64	0.671	283	305.31	-1.28	1.630
65 and older	0.121	47	55.06	-1.09	1.179
total	1.000	455	455		14.081

test statistic X² =14.081

c)

degree of freedom =categories-1=

3

d)

P-value < 0.005