Question

The following table shows age distribution and location of a random sample of 166 buffalo in a national park.

Age	Lamar District	Nez Perce District	Firehole District	Row Total
Calf	16	12	13	41
Yearling	10	12	11	33
Adult	30	31	31	92
Column Total	56

Use a chi-square test to determine if age distribution and location are independent at the 0.05 level of significance.

(a) What is the level of significance?

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State the null and alternate hypotheses.

H0: Age distribution and location are independent.

H1: Age distribution and location are not independent.

H0: Age distribution and location are not independent.

H1: Age distribution and location are not independent.

H0: Age distribution and location are not independent.

H1: Age distribution and location are independent.

H0: Age distribution and location are independent.

H1: Age distribution and location are independent.  

(b) 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.)

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Answer 1

The observed abd expected values are as below. Each expected value = Row total * Column Total / Total

Observed
	Lamar	Nez Perce	Firehole	Total
Calf	16	12	13	41
Yearling	10	12	11	33
Adult	30	31	31	92
Total	56	55	55	166
Expected
	Lamar	Nez Perce	Firehole	Total
Calf	13.831	13.584	13.584	40.999
Yearling	11.133	10.934	10.934	33.001
Adult	31.036	30.482	30.482	92
Total	56	55	55	166

(a) The Level of significance = 0.05

The Hypothesis: Option 1

H0: Age distribution and location are independent.

H1: Age distribution and location are not independent.

(b) The Test Statistic:

#	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	16	13.831	2.169	4.704561	0.340146
2	10	11.133	-1.133	1.283689	0.115305
3	30	31.036	-1.036	1.073296	0.034582
4	12	13.584	-1.584	2.509056	0.184707
5	12	10.934	1.066	1.136356	0.103929
6	31	30.482	0.518	0.268324	0.008803
7	13	13.584	-0.584	0.341056	0.025107
8	11	10.934	0.066	0.004356	0.000398
9	31	30.482	0.518	0.268324	0.008803
Total					0.822

= 0.822