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	13	13	15	41
Yearling	13	11	9	33
Adult	35	28	29	92
Column Total	61	52	53	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 not independent.
H₁: Age distribution and location are independent.

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

Yes

No    

What sampling distribution will you use?

binomialStudent's t    

normal

uniform

chi-square

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 > 0.100

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

(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

The statistical software output for this problem is:

Hence,

a) Level of significance = 0.05

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

Option D is correct.

b) Test statistic = 0.963

Yes

Chi - square

Degrees of freedom = 4

c) p-value > 0.100

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.