### Section: Hypothesis Testing **Task c: Compute the Value of the Test Statistic** - **Instruction:** (Round your answer to 2 decimal places.) - **Input Box:** Value of the test statistic [__________] **Task d: Substantiate Income Differences** - **Question:** Is there enough evidence to substantiate that residents of Wilmington, Delaware, have more income than the national average at the 0.025 significance level? - **Input Box Structure:** - **H₀:** There is [__________] evidence to conclude that the mean income in Wilmington is [__________] $37,000. **Navigation:** - **Note:** This is Page 7 of 9. - **Buttons:** [Prev] [Next] --- The tasks guide the user through statistical hypothesis testing. Task c involves computing a test statistic, while task d examines the evidence regarding income levels in Wilmington, Delaware. **Sample Hypothesis Tests** The mean income per person in the United States is $37,000, and the distribution of incomes follows a normal distribution. A random sample of 11 residents of Wilmington, Delaware, had a mean of $43,000 with a standard deviation of $8,800. At the 0.025 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average? a. State the null hypothesis and the alternate hypothesis. - **H₀ (Null Hypothesis):** μ ≤ [Blank] - **H₁ (Alternate Hypothesis):** μ > [Blank] b. State the decision rule for 0.025 significance level. *(Round your answer to 3 decimal places.)* - **Reject H₀ if t > [Blank]** (There is no graph or diagram in the image.)
### Section: Hypothesis Testing **Task c: Compute the Value of the Test Statistic** - **Instruction:** (Round your answer to 2 decimal places.) - **Input Box:** Value of the test statistic [__________] **Task d: Substantiate Income Differences** - **Question:** Is there enough evidence to substantiate that residents of Wilmington, Delaware, have more income than the national average at the 0.025 significance level? - **Input Box Structure:** - **H₀:** There is [__________] evidence to conclude that the mean income in Wilmington is [__________] $37,000. **Navigation:** - **Note:** This is Page 7 of 9. - **Buttons:** [Prev] [Next] --- The tasks guide the user through statistical hypothesis testing. Task c involves computing a test statistic, while task d examines the evidence regarding income levels in Wilmington, Delaware. **Sample Hypothesis Tests** The mean income per person in the United States is $37,000, and the distribution of incomes follows a normal distribution. A random sample of 11 residents of Wilmington, Delaware, had a mean of $43,000 with a standard deviation of $8,800. At the 0.025 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average? a. State the null hypothesis and the alternate hypothesis. - **H₀ (Null Hypothesis):** μ ≤ [Blank] - **H₁ (Alternate Hypothesis):** μ > [Blank] b. State the decision rule for 0.025 significance level. *(Round your answer to 3 decimal places.)* - **Reject H₀ if t > [Blank]** (There is no graph or diagram in the image.)
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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![### Section: Hypothesis Testing
**Task c: Compute the Value of the Test Statistic**
- **Instruction:** (Round your answer to 2 decimal places.)
- **Input Box:** Value of the test statistic [__________]
**Task d: Substantiate Income Differences**
- **Question:** Is there enough evidence to substantiate that residents of Wilmington, Delaware, have more income than the national average at the 0.025 significance level?
- **Input Box Structure:**
- **H₀:** There is [__________] evidence to conclude that the mean income in Wilmington is [__________] $37,000.
**Navigation:**
- **Note:** This is Page 7 of 9.
- **Buttons:** [Prev] [Next]
---
The tasks guide the user through statistical hypothesis testing. Task c involves computing a test statistic, while task d examines the evidence regarding income levels in Wilmington, Delaware.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66ecb00c-b439-47e9-bd51-9291e606d6a9%2F42c610a5-0112-4984-809b-d8a80a51b9ef%2Fjy51wcp.jpeg&w=3840&q=75)
Transcribed Image Text:### Section: Hypothesis Testing
**Task c: Compute the Value of the Test Statistic**
- **Instruction:** (Round your answer to 2 decimal places.)
- **Input Box:** Value of the test statistic [__________]
**Task d: Substantiate Income Differences**
- **Question:** Is there enough evidence to substantiate that residents of Wilmington, Delaware, have more income than the national average at the 0.025 significance level?
- **Input Box Structure:**
- **H₀:** There is [__________] evidence to conclude that the mean income in Wilmington is [__________] $37,000.
**Navigation:**
- **Note:** This is Page 7 of 9.
- **Buttons:** [Prev] [Next]
---
The tasks guide the user through statistical hypothesis testing. Task c involves computing a test statistic, while task d examines the evidence regarding income levels in Wilmington, Delaware.
![**Sample Hypothesis Tests**
The mean income per person in the United States is $37,000, and the distribution of incomes follows a normal distribution. A random sample of 11 residents of Wilmington, Delaware, had a mean of $43,000 with a standard deviation of $8,800. At the 0.025 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?
a. State the null hypothesis and the alternate hypothesis.
- **H₀ (Null Hypothesis):** μ ≤ [Blank]
- **H₁ (Alternate Hypothesis):** μ > [Blank]
b. State the decision rule for 0.025 significance level. *(Round your answer to 3 decimal places.)*
- **Reject H₀ if t > [Blank]**
(There is no graph or diagram in the image.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66ecb00c-b439-47e9-bd51-9291e606d6a9%2F42c610a5-0112-4984-809b-d8a80a51b9ef%2Fgycxk5o.jpeg&w=3840&q=75)
Transcribed Image Text:**Sample Hypothesis Tests**
The mean income per person in the United States is $37,000, and the distribution of incomes follows a normal distribution. A random sample of 11 residents of Wilmington, Delaware, had a mean of $43,000 with a standard deviation of $8,800. At the 0.025 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?
a. State the null hypothesis and the alternate hypothesis.
- **H₀ (Null Hypothesis):** μ ≤ [Blank]
- **H₁ (Alternate Hypothesis):** μ > [Blank]
b. State the decision rule for 0.025 significance level. *(Round your answer to 3 decimal places.)*
- **Reject H₀ if t > [Blank]**
(There is no graph or diagram in the image.)
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