The following table shows age distribution and location of a random sample of 166 buffalo in a national park. Lamar District Nez Perce District Firehole District Row Total 13 41 10 33 29 52 Age Calf Yearling Adult Column Total USE SALT 15 10 31 56 13 13 32 58 92 166 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?

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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The following table shows age distribution and location of a random sample of 166 buffalo in a national park.
Nez Perce District Firehole District Row Total
13
10
Age
Calf
Yearling
Adult
Column Total
USE SALT
Lamar District
15
10
31
56
State the null and alternate hypotheses.
O Ho: Age distribution and location are independent.
H₁: Age distribution and location are independent.
O Ho: Age distribution and location are not independent.
H₁: Age distribution and location are not independent.
29
52
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?
O Ho: Age distribution and location are not independent.
H₁: Age distribution and location are independent.
O Ho: Age distribution and location are independent.
H₁: Age distribution and location are not independent.
Are all the expected frequencies greater than 5?
O Yes
O No
What sampling distribution will you use?
O Student's t
O binomial
O uniform
O normal
O chi-square
13
13
32
58
What are the degrees of freedom?
41
33
(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.)
92
166
Transcribed Image Text:The following table shows age distribution and location of a random sample of 166 buffalo in a national park. Nez Perce District Firehole District Row Total 13 10 Age Calf Yearling Adult Column Total USE SALT Lamar District 15 10 31 56 State the null and alternate hypotheses. O Ho: Age distribution and location are independent. H₁: Age distribution and location are independent. O Ho: Age distribution and location are not independent. H₁: Age distribution and location are not independent. 29 52 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? O Ho: Age distribution and location are not independent. H₁: Age distribution and location are independent. O Ho: Age distribution and location are independent. H₁: Age distribution and location are not independent. Are all the expected frequencies greater than 5? O Yes O No What sampling distribution will you use? O Student's t O binomial O uniform O normal O chi-square 13 13 32 58 What are the degrees of freedom? 41 33 (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.) 92 166
(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)
O p-value > 0.100
O 0.050 < p-value < 0.100
0.025 < p-value < 0.050
0.010 < p-value < 0.025
O 0.005 < p-value < 0.010
O 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 > a, we fail to reject the null hypothesis.
Since the P-value > a, we reject the null hypothesis.
Since the P-value ≤ a, we reject the null hypothesis.
Since the P-values a, we fail to reject the null hypothesis.
(e) Interpret your conclusion in the context of the application.
O At the 5% level of significance, there is sufficient evidence to conclude that age distribution and location are not independent.
O At the 5% level of significance, there is insufficient evidence to conclude that age distribution and location are not independent.
Transcribed Image Text:(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) O p-value > 0.100 O 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 O 0.005 < p-value < 0.010 O 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 > a, we fail to reject the null hypothesis. Since the P-value > a, we reject the null hypothesis. Since the P-value ≤ a, we reject the null hypothesis. Since the P-values a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is sufficient evidence to conclude that age distribution and location are not independent. O At the 5% level of significance, there is insufficient evidence to conclude that age distribution and location are not independent.
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