Don’t know how to solve **Hypothesis Testing: Comparing Two Means**Assume both follow a Normal distribution. What can be concluded at the α = 0.01 level of significance?**Instructions**: Round all answers to 4 decimal places where possible.**Step (1)**: Determine the null and alternative hypotheses.- **Null Hypothesis (H₀)**: μ₁ = μ₂- **Alternative Hypothesis (Hₐ)**: μ₁ < μ₂**Step (2)**: Determine the test statistic and p-value.- **Test Statistic (t)**: 3.8232- **p-value**: 0.0007**Step (3)**: Find the critical value for the rejection region. Use:- **Critical Value (tᵥ)**: 2.583**Decision**: Make a decision using the rejection region method.- Reject the null hypothesis.(Reject the null hypothesis since the test statistic falls in the rejection region.)**Step (4)**: Compare the p-value to alpha (α).- **P-value ≤ α**Since the p-value is less than or equal to the significance level (α = 0.01), we reject the null hypothesis. Thus, there is sufficient evidence to conclude that μ₁ is less than μ₂ at the 0.01 level of significance. **Title: Statistical Analysis of Volunteer Hours Among Fraternity Brothers and Sorority Sisters**---**Introduction:**Members of fraternities and sororities are required to volunteer for community service. This study examines whether fraternity brothers work fewer volunteer hours on average compared to sorority sisters. The data presented includes the number of volunteer hours worked by nine randomly selected fraternity brothers and nine randomly selected sorority sisters. Both populations are assumed to be normally distributed, and the average of the fraternity brothers is the reference point.**Data:**- **Brothers' Volunteer Hours:** 9, 13, 14, 10, 7, 9, 15, 16, 5- **Sisters' Volunteer Hours:** 15, 16, 18, 11, 14, 20, 13, 19, 17**Hypothesis Testing:**We are conducting a hypothesis test to determine whether there is a significant difference in the average volunteer hours between fraternity brothers and sorority sisters at the 0.01 level of significance.**Statistical Test:**- **Step 1:** Determine the Null and Alternative Hypotheses. - **\(H_0\):** \( \mu_1 = \mu_2 \) (The average volunteer hours for fraternity brothers and sorority sisters are equal.) - **\(H_a\):** \( \mu_1 \neq \mu_2 \) (The average volunteer hours for fraternity brothers and sorority sisters are not equal.)**Instructions:**Round all answers to four decimal places where possible.---**Graph/Diagram Explanation:**In this section, a table is provided:- **Left Column:** Lists the volunteer hours for fraternity brothers. - **Right Column:** Lists the volunteer hours for sorority sisters.The analysis involves comparing these data sets to determine any statistically significant differences in their means.---

Given: n1 = 10 n2 = 10 α = 0.01 Formula Used: Test-statistic t = X1-X2sp1n1+1n2 sp =…

Assume both follow a Normal distribution. What can be concluded at the a = .01 level of significance? Round all answers to 4 places where possible. Step (1) Determine the null and alternative hypotheses. Ho: 1 Ha: μ1 Step (2) Determine the test statistic and p-value. Test Statistic: t = 3.8232 p-value = 0.0007 tv = 2.583 Step (3) Find the critical value for the rejection region (Use 林 Reject the null hypothesis. O Fail to reject the null hypothesis. Make a decision using the rejection region method. Step (4) Compare the p-value to alpha P-value s 2 38 ✔✔¤ μ2

Assume both follow a Normal distribution. What can be concluded at the a = .01 level of significance? Round all answers to 4 places where possible. Step (1) Determine the null and alternative hypotheses. Ho: 1 Ha: μ1 Step (2) Determine the test statistic and p-value. Test Statistic: t = 3.8232 p-value = 0.0007 tv = 2.583 Step (3) Find the critical value for the rejection region (Use 林 Reject the null hypothesis. O Fail to reject the null hypothesis. Make a decision using the rejection region method. Step (4) Compare the p-value to alpha P-value s 2 38 ✔✔¤ μ2

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

Don’t know how to solve

**Hypothesis Testing: Comparing Two Means**

Assume both follow a Normal distribution. What can be concluded at the α = 0.01 level of significance?

**Instructions**: Round all answers to 4 decimal places where possible.

**Step (1)**: Determine the null and alternative hypotheses.

- **Null Hypothesis (H₀)**: μ₁ = μ₂
- **Alternative Hypothesis (Hₐ)**: μ₁ < μ₂

**Step (2)**: Determine the test statistic and p-value.

- **Test Statistic (t)**: 3.8232
- **p-value**: 0.0007

**Step (3)**: Find the critical value for the rejection region. Use:

- **Critical Value (tᵥ)**: 2.583

**Decision**: Make a decision using the rejection region method.

- Reject the null hypothesis.

(Reject the null hypothesis since the test statistic falls in the rejection region.)

**Step (4)**: Compare the p-value to alpha (α).

- **P-value ≤ α**

Since the p-value is less than or equal to the significance level (α = 0.01), we reject the null hypothesis. Thus, there is sufficient evidence to conclude that μ₁ is less than μ₂ at the 0.01 level of significance.

**Title: Statistical Analysis of Volunteer Hours Among Fraternity Brothers and Sorority Sisters**

---

**Introduction:**

Members of fraternities and sororities are required to volunteer for community service. This study examines whether fraternity brothers work fewer volunteer hours on average compared to sorority sisters. The data presented includes the number of volunteer hours worked by nine randomly selected fraternity brothers and nine randomly selected sorority sisters. Both populations are assumed to be normally distributed, and the average of the fraternity brothers is the reference point.

**Data:**

- **Brothers' Volunteer Hours:** 9, 13, 14, 10, 7, 9, 15, 16, 5

- **Sisters' Volunteer Hours:** 15, 16, 18, 11, 14, 20, 13, 19, 17

**Hypothesis Testing:**

We are conducting a hypothesis test to determine whether there is a significant difference in the average volunteer hours between fraternity brothers and sorority sisters at the 0.01 level of significance.

**Statistical Test:**

- **Step 1:** Determine the Null and Alternative Hypotheses.

- **\(H_0\):** \( \mu_1 = \mu_2 \) (The average volunteer hours for fraternity brothers and sorority sisters are equal.)

- **\(H_a\):** \( \mu_1 \neq \mu_2 \) (The average volunteer hours for fraternity brothers and sorority sisters are not equal.)

**Instructions:**

Round all answers to four decimal places where possible.

---

**Graph/Diagram Explanation:**

In this section, a table is provided:

- **Left Column:** Lists the volunteer hours for fraternity brothers.

- **Right Column:** Lists the volunteer hours for sorority sisters.

The analysis involves comparing these data sets to determine any statistically significant differences in their means.

---

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