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 12 11 18 41 Yearling 10 10 13 33 Adult 32 27 33 92 Column Total 54 48 64 166 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 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 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? YesNo What sampling distribution will you use? chi-squareuniform normalbinomialStudent'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 > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, 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.

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 12 11 18 41 Yearling 10 10 13 33 Adult 32 27 33 92 Column Total 54 48 64 166 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 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 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? YesNo What sampling distribution will you use? chi-squareuniform normalbinomialStudent'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 > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, 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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	12	11	18	41
Yearling	10	10	13	33
Adult	32	27	33	92
Column Total	54	48	64	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 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 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?

YesNo

What sampling distribution will you use?

chi-squareuniform normalbinomialStudent'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 > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, 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.

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