Was stuck on how to set up and what sets are needed **Hypothesis Testing for GPA Concerns at City University**In this scenario, the Chancellor at City University is concerned about a potential decline in student GPAs over the past year. Historically, the GPA for graduating students over the last five years has been 2.80, with a standard deviation of 0.25. To investigate, the Chancellor collected GPAs from a random sample of 10 seniors from this year's graduating class:- Sampled GPAs: 2.40, 2.80, 2.65, 2.15, 2.65, 2.72, 2.42, 2.70, 2.52, 2.49**Objective:**Determine whether there is statistically significant evidence to conclude that the average GPA has decreased. Conduct a one-tailed test at the 0.05 significance level.**Steps to Conduct the Hypothesis Test:**1. **State the Hypotheses:** - Null Hypothesis (H0): μ = 2.80 (The mean GPA has not decreased.) - Alternative Hypothesis (H1): μ < 2.80 (The mean GPA has decreased.)2. **Select the Significance Level:** - α = 0.053. **Calculate the Test Statistic:** - Use the sample mean ($\bar{x}$) and standard deviation (s) to calculate the t-statistic.4. **Determine the Decision Rule:** - Find the critical t-value from the t-distribution table with n-1 degrees of freedom (where n is the sample size). - If the calculated t-statistic is less than the critical t-value, reject the null hypothesis.5. **Make a Decision:** - Compare the calculated t-statistic with the critical t-value to decide whether to reject or fail to reject the null hypothesis.6. **Conclusion:** - Interpret the results in the context of the problem, indicating whether there is evidence to support the Chancellor's concern about declining GPAs.

Answered: Image /qna-images/answer/2926b79e-e8bd-4ac0-ab0f-6166cc797a28.jpg

The chancellor at City University is worried that the grades have fallen in past year. The grade point average for graduating students in the previous s was 2.80 with a standard deviation of 0.25. The chancellor randoml- ples 10 seniors from this year's graduating class and obtains the following s: 2.40, 2.80, 2.65, 2.15, 2.65, 2.72, 2.42, 2.70, 2.52, 2.49. What can the cellor conclude? Use a one-tailed test at the .05 significance level. Show lahel all stens of vour bvnothesis test

The chancellor at City University is worried that the grades have fallen in past year. The grade point average for graduating students in the previous s was 2.80 with a standard deviation of 0.25. The chancellor randoml- ples 10 seniors from this year's graduating class and obtains the following s: 2.40, 2.80, 2.65, 2.15, 2.65, 2.72, 2.42, 2.70, 2.52, 2.49. What can the cellor conclude? Use a one-tailed test at the .05 significance level. Show lahel all stens of vour bvnothesis test

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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Question

Was stuck on how to set up and what sets are needed

**Hypothesis Testing for GPA Concerns at City University**

In this scenario, the Chancellor at City University is concerned about a potential decline in student GPAs over the past year. Historically, the GPA for graduating students over the last five years has been 2.80, with a standard deviation of 0.25. To investigate, the Chancellor collected GPAs from a random sample of 10 seniors from this year's graduating class:

- Sampled GPAs: 2.40, 2.80, 2.65, 2.15, 2.65, 2.72, 2.42, 2.70, 2.52, 2.49

**Objective:**

Determine whether there is statistically significant evidence to conclude that the average GPA has decreased. Conduct a one-tailed test at the 0.05 significance level.

**Steps to Conduct the Hypothesis Test:**

1. **State the Hypotheses:**
- Null Hypothesis (H0): μ = 2.80 (The mean GPA has not decreased.)
- Alternative Hypothesis (H1): μ < 2.80 (The mean GPA has decreased.)

2. **Select the Significance Level:**
- α = 0.05

3. **Calculate the Test Statistic:**
- Use the sample mean ($\bar{x}$) and standard deviation (s) to calculate the t-statistic.

4. **Determine the Decision Rule:**
- Find the critical t-value from the t-distribution table with n-1 degrees of freedom (where n is the sample size).
- If the calculated t-statistic is less than the critical t-value, reject the null hypothesis.

5. **Make a Decision:**
- Compare the calculated t-statistic with the critical t-value to decide whether to reject or fail to reject the null hypothesis.

6. **Conclusion:**
- Interpret the results in the context of the problem, indicating whether there is evidence to support the Chancellor's concern about declining GPAs.

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