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 12 15 41 Yearling 13 11 9 33 Adult 35 30 27 92 Column Total 62 53 51 166 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? Yes No What sampling distribution will you use? Student's t chi-square binomial uniform normal 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

a) e 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	Firehole	Total
	Calf	15.313	13.090	12.596	41
	Yearling	12.325	10.536	10.139	33
	Adult	34.361	29.373	28.265	92
	total	62	53	51	166
chi square    χ2	=(Oi-Ei)2/Ei	Lamar	Nez	Firehole	Total
	Calf	0.113	0.091	0.459	0.6621
	Yearling	0.037	0.020	0.128	0.1852
	Adult	0.012	0.013	0.057	0.0818
	total	0.1614	0.1246	0.6431	0.929
test statistic X2 =		0.929

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 > 0.100

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.