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	15	12	14	41
Yearling	13	11	9	33
Adult	31	28	33	92
Column Total	59	51	56	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 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.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

binomialchi-square    uniformnormalStudent'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

(a)

Level of significance = 0.05

Correct option :

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

(b)

Value of the chi-square statistic for the sample = 0.877

Yes, all the expected frequencies are greater than 5

Sampling distribution : Chi Square

Degrees of freedom = (3-1)*(3-1) = 2*2 = 4

(c)

Correct option : p-value > 0.100

(d)

Correct option : Since the P-value > , we fail to reject the null hypothesis.

(e)

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