Help! **Testing Salary Differences: Tampa vs. Dallas Nurses**An article published by The Florida Tribune claimed that nurses in Tampa earn more than nurses in Dallas. As a manager at a Tampa hospital, you are interested in testing this claim at a significance level of $ \alpha = 0.05 $. You conducted a survey with a sample of 41 nurses in Tampa and 50 nurses in Dallas. Here are the findings:- The Tampa sample: - Average salary: $63,200 - Standard deviation: $5,300- The Dallas sample: - Average salary: $60,700 - Standard deviation: $4,800### Hypotheses- **Null Hypothesis (H₀):** $ \mu_{1} - \mu_{2} = 0 $ - There is no difference in the average salaries between nurses in Tampa and Dallas.- **Alternative Hypothesis (Hₐ):** $ \mu_{1} - \mu_{2} > 0 $ - Nurses in Tampa earn more than nurses in Dallas.*Note: In this setup, Sample 1 (Tampa) and Sample 2 (Dallas).*### Questions:a) **What is the test statistic?**b) **What is the p-value?**c) **State your conclusion (in the context of the problem).**### Detailed ExplanationTo test this hypothesis, we use a two-sample t-test to determine if there is a statistically significant difference between the salaries of nurses in both locations. Calculate the test statistic (a), the p-value (b), and then draw a conclusion based on these results (c). This test helps you make an informed decision about the claim made by The Florida Tribune regarding nurse salaries in Tampa and Dallas.

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The Florida Tribune published an article that claimed that nurses in Tampa earn more than nurses in Dallas. You are a manager at a Tampa hospital and want to test the claim of the Tribune. You wish to test the claim at a significance level of a=0.05. So you conduct a follow up survey of 41 nurses in Tampa and 50 nurses in Dallas. You find that the sample from Tampa showed an average salary of $63200 with a standard deviation of 5300, and the sample from Dallas showed an average salary of $60700 with a standard deviation of 4800. Our claims are: Ho: µ1 – H2 = 0 Ha: H1 – Hz > 0 (in this setup, sample 1 is the group of nurses from Tampa and sample 2 is the group of nurses from Dallas) a) What is the test statistic? b) What is the p-value? c) State your conclusion (in the context of the problem).

The Florida Tribune published an article that claimed that nurses in Tampa earn more than nurses in Dallas. You are a manager at a Tampa hospital and want to test the claim of the Tribune. You wish to test the claim at a significance level of a=0.05. So you conduct a follow up survey of 41 nurses in Tampa and 50 nurses in Dallas. You find that the sample from Tampa showed an average salary of $63200 with a standard deviation of 5300, and the sample from Dallas showed an average salary of $60700 with a standard deviation of 4800. Our claims are: Ho: µ1 – H2 = 0 Ha: H1 – Hz > 0 (in this setup, sample 1 is the group of nurses from Tampa and sample 2 is the group of nurses from Dallas) a) What is the test statistic? b) What is the p-value? c) State your conclusion (in the context of the problem).

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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Help!

**Testing Salary Differences: Tampa vs. Dallas Nurses**

An article published by The Florida Tribune claimed that nurses in Tampa earn more than nurses in Dallas. As a manager at a Tampa hospital, you are interested in testing this claim at a significance level of $ \alpha = 0.05 $. You conducted a survey with a sample of 41 nurses in Tampa and 50 nurses in Dallas. Here are the findings:

- The Tampa sample:
- Average salary: $63,200
- Standard deviation: $5,300

- The Dallas sample:
- Average salary: $60,700
- Standard deviation: $4,800

### Hypotheses
- **Null Hypothesis (H₀):** $ \mu_{1} - \mu_{2} = 0 $
- There is no difference in the average salaries between nurses in Tampa and Dallas.
- **Alternative Hypothesis (Hₐ):** $ \mu_{1} - \mu_{2} > 0 $
- Nurses in Tampa earn more than nurses in Dallas.

*Note: In this setup, Sample 1 (Tampa) and Sample 2 (Dallas).*

### Questions:
a) **What is the test statistic?**

b) **What is the p-value?**

c) **State your conclusion (in the context of the problem).**

### Detailed Explanation

To test this hypothesis, we use a two-sample t-test to determine if there is a statistically significant difference between the salaries of nurses in both locations. Calculate the test statistic (a), the p-value (b), and then draw a conclusion based on these results (c). This test helps you make an informed decision about the claim made by The Florida Tribune regarding nurse salaries in Tampa and Dallas.

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