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 13 13 41 Yearling 11 10 12 33 Adult 33 24 35 92 Column Total 59 47 60 166 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 not independent. 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. (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's tnormal chi-squarebinomialuniform 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

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 6E: List the sample space of each experiment. Tossing three coins

See similar textbooks

Related questions

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	13	13	41
Yearling	11	10	12	33
Adult	33	24	35	92
Column Total	59	47	60	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 not independent. 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.

(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's tnormal chi-squarebinomialuniform

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.

Expert Solution

Step by step

Solved in 4 steps with 6 images

SEE SOLUTION Check out a sample Q&A here