In response to a complaint that a particular tax assessor (1) was biased, an experiment was conducted to compare the assessor named in the complaint with another tax assessor (2) from the same office. Eight properties were selected, and each was assessed by both assessors. The assessments (in thousands of dollars) are shown in the table.
In response to a complaint that a particular tax assessor (1) was biased, an experiment was conducted to compare the assessor named in the complaint with another tax assessor (2) from the same office. Eight properties were selected, and each was assessed by both assessors. The assessments (in thousands of dollars) are shown in the table.
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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I need help with all parts of this question 17
![### Statistical Analysis Exercise
#### (a) Hypothesis Testing
**Objective:**
Determine if there is sufficient evidence to suggest that Assessor 1 tends to give higher assessments than Assessor 2. The significance level is \(\alpha = 0.05\).
**Hypotheses:**
Choose the appropriate null and alternative hypotheses:
- \( H_0: \mu_d \neq 0 \) versus \( H_a: \mu_d = 0 \)
- \( H_0: \mu_d = 0 \) versus \( H_a: \mu_d \neq 0 \)
- \( H_0: \mu_d < 0 \) versus \( H_a: \mu_d > 0 \)
- \( H_0: \mu_d = 0 \) versus \( H_a: \mu_d > 0 \)
- \( H_0: \mu_d = 0 \) versus \( H_a: \mu_d < 0 \)
**Test Statistic:**
Enter the calculated test statistic value.
\[ t = \text{_____} \]
**P-value:**
Enter the p-value.
\[ \text{P-value: _____} \]
**Conclusion:**
Choose the conclusion based on the results:
- \( H_0 \) is not rejected. There is sufficient evidence to indicate Assessor A gives higher assessments than Assessor B.
- \( H_0 \) is rejected. There is insufficient evidence to indicate Assessor A gives higher assessments than Assessor B.
- \( H_0 \) is rejected. There is sufficient evidence to indicate Assessor A gives higher assessments than Assessor B.
- \( H_0 \) is not rejected. There is insufficient evidence to indicate Assessor A gives higher assessments than Assessor B.
#### (b) Confidence Interval
**95% Lower One-Sided Confidence Bound:**
Estimate using \((\mu_1 - \mu_2)\).
\[ \text{Estimate: _____} \]
#### (c) Assumptions
**Required Assumptions:**
Select all assumptions that must be valid for the inference in parts (a) and (b):
- \(\square\) The properties must be randomly selected.
- \(\square\) The properties must be independently selected.
- \(\square\) The sample size must be greater than 5 for each assessor.
- \(\square\) The](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9175f245-2e1a-4def-805b-da74e3897838%2Fccbd0f06-b80c-4660-884c-5ef8fda80051%2Fqwz8y7r_processed.png&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis Exercise
#### (a) Hypothesis Testing
**Objective:**
Determine if there is sufficient evidence to suggest that Assessor 1 tends to give higher assessments than Assessor 2. The significance level is \(\alpha = 0.05\).
**Hypotheses:**
Choose the appropriate null and alternative hypotheses:
- \( H_0: \mu_d \neq 0 \) versus \( H_a: \mu_d = 0 \)
- \( H_0: \mu_d = 0 \) versus \( H_a: \mu_d \neq 0 \)
- \( H_0: \mu_d < 0 \) versus \( H_a: \mu_d > 0 \)
- \( H_0: \mu_d = 0 \) versus \( H_a: \mu_d > 0 \)
- \( H_0: \mu_d = 0 \) versus \( H_a: \mu_d < 0 \)
**Test Statistic:**
Enter the calculated test statistic value.
\[ t = \text{_____} \]
**P-value:**
Enter the p-value.
\[ \text{P-value: _____} \]
**Conclusion:**
Choose the conclusion based on the results:
- \( H_0 \) is not rejected. There is sufficient evidence to indicate Assessor A gives higher assessments than Assessor B.
- \( H_0 \) is rejected. There is insufficient evidence to indicate Assessor A gives higher assessments than Assessor B.
- \( H_0 \) is rejected. There is sufficient evidence to indicate Assessor A gives higher assessments than Assessor B.
- \( H_0 \) is not rejected. There is insufficient evidence to indicate Assessor A gives higher assessments than Assessor B.
#### (b) Confidence Interval
**95% Lower One-Sided Confidence Bound:**
Estimate using \((\mu_1 - \mu_2)\).
\[ \text{Estimate: _____} \]
#### (c) Assumptions
**Required Assumptions:**
Select all assumptions that must be valid for the inference in parts (a) and (b):
- \(\square\) The properties must be randomly selected.
- \(\square\) The properties must be independently selected.
- \(\square\) The sample size must be greater than 5 for each assessor.
- \(\square\) The
Transcribed Image Text:In response to a complaint that a particular tax assessor (1) was biased, an experiment was conducted to compare the assessor named in the complaint with another tax assessor (2) from the same office. Eight properties were selected, and each was assessed by both assessors. The assessments (in thousands of dollars) are shown in the table.
| Property | Assessor 1 | Assessor 2 |
|----------|------------|------------|
| 1 | 277.1 | 275.8 |
| 2 | 287.9 | 287.5 |
| 3 | 276.3 | 276.5 |
| 4 | 295.0 | 290.8 |
| 5 | 295.9 | 296.9 |
| 6 | 281.9 | 281.9 |
| 7 | 276.5 | 275.0 |
| 8 | 279.1 | 278.5 |
Use the MINITAB printout to answer the questions that follow. (Use the exact values found in the MINITAB output.)
**Paired T-Test and CI: Assessor 1, Assessor 2**
Descriptive Statistics
- **Sample**
- **N**: 8
- **Mean**:
- Assessor 1: 280.91
- Assessor 2: 279.48
- **StDev**:
- Assessor 1: 9.71
- Assessor 2: 6.95
- **SE Mean**:
- Assessor 1: 2.73
- Assessor 2: 2.46
**Estimation for Paired Difference**
- **Mean**: 1.438
- **StDev**: 1.667
- **SE Mean**: 0.589
- **95% Lower Bound for μ_difference**: 0.321
\(\mu_{\text{difference}} = \text{mean of (Assessor 1 - Assessor 2)}\)
**Test**
- **Null Hypothesis**: \(H_0: \mu_{\text{difference}} = 0\)
- **Alternative Hypothesis**: \(H_
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