A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.01 years, with sample standard deviation s = 0.76 years. However, it is thought that the overall population mean age of coyotes is u = 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 Họ: H = 1.75 yr; H1: µ < 1.75 yr O Họ: H < 1.75 yr; H1: µ = 1.75 yr О Но: и> 1.75 уг;B Hi: и 1.75 уг О Hо: и 1.75 уг; H;: и > 1.75 yг О Hо: и 1.75 уг; H;: и * 1.75 уг (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 o is known. 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 unknown. O The Student's t, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find the P-value. (Round your answer to four decimal places.)
A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.01 years, with sample standard deviation s = 0.76 years. However, it is thought that the overall population mean age of coyotes is u = 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 Họ: H = 1.75 yr; H1: µ < 1.75 yr O Họ: H < 1.75 yr; H1: µ = 1.75 yr О Но: и> 1.75 уг;B Hi: и 1.75 уг О Hо: и 1.75 уг; H;: и > 1.75 yг О Hо: и 1.75 уг; H;: и * 1.75 уг (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 o is known. 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 unknown. O The Student's t, since the sample size is large and o is unknown. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find the P-value. (Round your answer to four decimal places.)
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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![**Statistical Analysis of Coyote Age in Northern Minnesota**
A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be \( \bar{x} = 2.01 \) years, with a sample standard deviation \( s = 0.76 \) years. The overall population mean age of coyotes is thought to be \( \mu = 1.75 \) years. 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 \( \alpha = 0.01 \).
### (a) Level of Significance
- **What is the level of significance?**
\[ \alpha = 0.01 \]
### State the Null and Alternative Hypotheses
1. \( H_0: \mu = 1.75 \, \text{yr}; \, H_1: \mu < 1.75 \, \text{yr} \)
2. \( H_0: \mu < 1.75 \, \text{yr}; \, H_1: \mu = 1.75 \, \text{yr} \)
3. \( H_0: \mu > 1.75 \, \text{yr}; \, H_1: \mu = 1.75 \, \text{yr} \)
4. \( H_0: \mu = 1.75 \, \text{yr}; \, H_1: \mu > 1.75 \, \text{yr} \)
5. \( H_0: \mu = 1.75 \, \text{yr}; \, H_1: \mu \neq 1.75 \, \text{yr} \)
### (b) Sampling Distribution
- **Which sampling distribution will you use? Explain the rationale for your choice of sampling distribution.**
- The Student's \( t \), since the sample size is large and \( \sigma \) is unknown.
- **What is the value of the sample test statistic? (Round your answer to three decimal places.)**
[Answer here]
### (c) Find the P-Value
- **Find the \( P \)-value. (Round your answer to four decimal places.)**
[Answer here]
This educational exercise illustrates](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F263d6acc-03b4-45b5-8ce2-d676aa9ac999%2Fefac93e4-81e2-43bd-8e5d-46e81554f8f0%2Ffkwn1gs_processed.png&w=3840&q=75)
Transcribed Image Text:**Statistical Analysis of Coyote Age in Northern Minnesota**
A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be \( \bar{x} = 2.01 \) years, with a sample standard deviation \( s = 0.76 \) years. The overall population mean age of coyotes is thought to be \( \mu = 1.75 \) years. 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 \( \alpha = 0.01 \).
### (a) Level of Significance
- **What is the level of significance?**
\[ \alpha = 0.01 \]
### State the Null and Alternative Hypotheses
1. \( H_0: \mu = 1.75 \, \text{yr}; \, H_1: \mu < 1.75 \, \text{yr} \)
2. \( H_0: \mu < 1.75 \, \text{yr}; \, H_1: \mu = 1.75 \, \text{yr} \)
3. \( H_0: \mu > 1.75 \, \text{yr}; \, H_1: \mu = 1.75 \, \text{yr} \)
4. \( H_0: \mu = 1.75 \, \text{yr}; \, H_1: \mu > 1.75 \, \text{yr} \)
5. \( H_0: \mu = 1.75 \, \text{yr}; \, H_1: \mu \neq 1.75 \, \text{yr} \)
### (b) Sampling Distribution
- **Which sampling distribution will you use? Explain the rationale for your choice of sampling distribution.**
- The Student's \( t \), since the sample size is large and \( \sigma \) is unknown.
- **What is the value of the sample test statistic? (Round your answer to three decimal places.)**
[Answer here]
### (c) Find the P-Value
- **Find the \( P \)-value. (Round your answer to four decimal places.)**
[Answer here]
This educational exercise illustrates
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