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	9	13	19	41
Yearling	10	10	13	33
Adult	36	26	30	92
Column Total	55	49	62	166

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

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


b) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > ?, we fail to reject the null hypothesis.

Since the P-value > ?, we reject the null hypothesis.    

Since the P-value ? ?, we reject the null hypothesis.

Since the P-value ? ?, we fail to reject the null hypothesis.

c) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that age distribution and location are not independent.

At the 5% level of significance, there is insufficient evidence to conclude that age distribution and location are not independent.    

Answer 1

here the expected table is given below.

Age	Lamar District	Nez Perce District	Firehole District	Row Total
Calf	13.58	12.10	15.31	41
Yearling	10.93	9.74	12.33	33
Adult	30.48	27.16	34.36	92
Column Total	55	55	55	165

Here the chi-square table is given below.

where

X² =

Age	Lamar District	Nez Perce District	Firehole District	Row Total
Calf	1.55	0.07	0.89	2.50
Yearling	0.08	0.01	0.04	0.12
Adult	1.00	0.05	0.55	1.60
Column Total	2.63	0.12	1.48	4.23

Here

p - value = Pr(X² > 4.23; dF = 2 * 2 = 4) = 0.3762

(b) Since the P-value > ?, we fail to reject the null hypothesis. Option A is correct.

(c) At the 5% level of significance, there is insufficient evidence to conclude that age distribution and location are not independent.