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	14	11	16	41
Yearling	11	10	12	33
Adult	34	27	31	92
Column Total	59	48	59	166

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?


State the null and alternate hypotheses.

H₀: Age distribution and location are not independent.
H₁: Age distribution and location are not independent.H₀: Age distribution and location are independent.
H₁: Age distribution and location are independent.    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 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.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

normaluniform    binomialchi-squareStudent's t

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.)

p-value > 0.1000.050 < p-value < 0.100    0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005

(d) 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 > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) 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

level of significance =0.05

H₀: Age distribution and location are independent.
H₁: Age distribution and location are not independent.

b)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Lamar	Nez Perce	Firehole	Total
	calf	14.57	11.86	14.57	41
	Yearling	11.73	9.54	11.73	33
	Adult	32.70	26.60	32.70	92
	total	59	48	59	166
chi square    χ2	=(Oi-Ei)2/Ei	Lamar	Nez Perce	Firehole	Total
	calf	0.0225	0.0617	0.1399	0.2241
	Yearling	0.0453	0.0220	0.0063	0.0735
	Adult	0.0518	0.0059	0.0883	0.1460
	total	0.1196	0.0896	0.2344	0.4436
test statistic X2 =		0.444

Are all the expected frequencies greater than 5? :Yes

What sampling distribution will you use? chi-square

degrees of freedom =(row-1)*(column-1)=4

c)

p-value > 0.10

d)

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

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