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	14	11	41
Yearling	10	12	11	33
Adult	35	32	25	92
Column Total	61	58	47	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 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 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?

chi-squarenormal     binomialuniformStudent'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

Expected count =

	Lamar District	Nez Perce District	Firehole District			Row Totals
Calf	16  (15.066)	14  (14.325)	11  (11.608)			41
Yearling	10  (12.126)	12  (11.530)	11  (9.343)			33
Adult	35  (33.807)	32  (32.146)	25  (26.048)			92
Column Totals	61	58	47			166  (Grand Total)

The contingency table below provides the following information: the observed cell totals, (the expected cell totals)

The chi-square statistic is 0.868.

(a) What is the level of significance?
level of significance = 0.05

null and alternate hypotheses.

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

b) The chi-square statistic is 0.868.

Yes all the expected frequencies greater than 5 .

We use chi-squarenormal sampling distribution.

degrees of freedom = (r-1)(c-1) = (3-1)(3-1) = 4

c) p-value is greater than 0.100

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.