The following table shows age distribution and location of arandom sample of 166 buffalo in a national park.

Age	LamarDistrict	Nez PerceDistrict	FireholeDistrict	RowTotal
Calf	15	13	13	41
Yearling	12	8	13	33
Adult	31	26	35	92
Column Total	58	47	61	166

Use a chi-square test to determine if age distribution andlocation 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 notindependent.
H₁: Age distribution and location are notindependent.H₀: Age distribution and locationare independent.
H₁: Age distribution and location are notindependent.    H₀: Agedistribution and location are not independent.
H₁: Age distribution and location areindependent.H₀: Age distribution and locationare independent.
H₁: Age distribution and location areindependent.

(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?

Student'stbinomial    normalchi-squareuniform

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample teststatistic. (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 orfail to reject the null hypothesis of independence?

Since the P-value > ?, we fail to rejectthe null hypothesis.Since the P-value > ?, wereject the null hypothesis.    Since theP-value ? ?, we reject the null hypothesis.Sincethe P-value ? ?, we fail to reject the nullhypothesis.

(e) Interpret your conclusion in the context of theapplication.

At the 5% level of significance, there is sufficient evidence toconclude that age distribution and location are not independent.Atthe 5% level of significance, there is insufficient evidence toconclude that age distribution and location are notindependent.