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A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.03 years, with sample standard deviation s= 0.78 years. However, it is thought that the overall population mean age of coyotes is = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: = 1.75 yr; H₁: # < 1.75 yr O Ho: = 1.75 yr; H₁: ## 1.75 yr Ho: < 1.75 yr; H₁: = 1.75 yr 1.75 yr; H₁: μ > 1.75 yr Ho: O Ho: > 1.75 yr; H₁: = 1.75 yr (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and a is known. O The standard normal, since the sample size is large and o is known. 4

A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.03 years, with sample standard deviation s= 0.78 years. However, it is thought that the overall population mean age of coyotes is = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: = 1.75 yr; H₁: # < 1.75 yr O Ho: = 1.75 yr; H₁: ## 1.75 yr Ho: < 1.75 yr; H₁: = 1.75 yr 1.75 yr; H₁: μ > 1.75 yr Ho: O Ho: > 1.75 yr; H₁: = 1.75 yr (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and a is known. O The standard normal, since the sample size is large and o is known. 4

MATLAB: An Introduction with Applications
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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= A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x 2.03 years, with sample standard deviation s = 0.78 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: μ = 1.75 yr; H₁: < 1.75 yr O Ho: μ = 1.75 yr; H₁: μ ‡ 1.75 yr O Ho: μ< 1.75 yr; H₁: μ = 1.75 yr Ho: μ = 1.75 yr; H₁: μ > 1.75 yr O Ho: μ> 1.75 yr; H₁: μ = 1.75 yr (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and σ is unknown. O The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is known. 10 (c) Estimate the P-value. OP-value > 0.250 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O P-value < 0.010 2000-4-40-10 P 30-09-1 What is the value of the sample test statistic? (Round your answer to three decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. 7:14 P
Transcribed Image Text:= A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x 2.03 years, with sample standard deviation s = 0.78 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: μ = 1.75 yr; H₁: < 1.75 yr O Ho: μ = 1.75 yr; H₁: μ ‡ 1.75 yr O Ho: μ< 1.75 yr; H₁: μ = 1.75 yr Ho: μ = 1.75 yr; H₁: μ > 1.75 yr O Ho: μ> 1.75 yr; H₁: μ = 1.75 yr (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since the sample size is large and a is unknown. O The Student's t, since the sample size is large and σ is unknown. O The Student's t, since the sample size is large and o is known. O The standard normal, since the sample size is large and o is known. 10 (c) Estimate the P-value. OP-value > 0.250 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O P-value < 0.010 2000-4-40-10 P 30-09-1 What is the value of the sample test statistic? (Round your answer to three decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. 7:14 P
Sketch the sampling distribution and show the area corresponding to the P-value. O -2 -2 0 0 2 2 4 4 T -2 -2 0 2 2 4 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. O There is sufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years. O There is insufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years. 4
Transcribed Image Text:Sketch the sampling distribution and show the area corresponding to the P-value. O -2 -2 0 0 2 2 4 4 T -2 -2 0 2 2 4 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) Interpret your conclusion in the context of the application. O There is sufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years. O There is insufficient evidence at the 0.01 level to conclude that coyotes in the specified region tend to live longer than 1.75 years. 4
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