to view the Student 1-distribution table. 2 H₁: Hy
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Hypothesis Testing and Confidence Interval Calculation for Two Populations
To solve these problems, follow the steps outlined below.
#### Assumptions:
- Both populations are normally distributed.
#### Given Data:
- **Sample 1**:
- \( n = 27 \)
- \( \overline{x} = 46.3 \)
- \( s = 9.1 \)
- **Sample 2**:
- \( n = 21 \)
- \( \overline{x} = 36.4 \)
- \( s = 8.7 \)
#### Tasks to Perform:
1. **Test whether \(\mu_1 > \mu_2\) at \(\alpha = 0.05\) level of significance for the given sample data.**
2. **Construct a 95% confidence interval about \(\mu_1 - \mu_2\).**
#### Procedure:
1. **Testing the Hypothesis: \( \mu_1 > \mu_2 \)**
**Hypotheses:**
- \( H_0: \mu_1 \leq \mu_2 \)
- \( H_1: \mu_1 > \mu_2 \)
2. **Determine the Test Statistic \( t \):**
\[
t = \text{(Round to two decimal places as needed.)}
\]
3. **Determine the Critical Value(s):**
- Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed).
- \( A. \) The critical value is
- \( B. \) The lower critical value is \_\_\_\_\_. The upper critical value is \_\_\_\_\_.
4. **Determine Whether the Hypothesis Should be Rejected:**
- Reject the null hypothesis because the test statistic \( \_\_\_\_\_\_\ ) the critical region.
### Constructing a 95% Confidence Interval for \( \mu_1 - \mu_2 \)
The confidence interval is the range from \[\_\_\_\_\_\_\_\] to \[\_\_\_\_\_\_\_\].
(Round to two decimal places as needed. Use ascending order.)
#### Graph Explanation:
There is an inserted window titled "Student t-Distribution Table" that shows critical t-values for various](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd86b4514-aa18-4e84-8d65-86fc6c642f07%2F26e9082a-570f-453f-90d9-ad1eb01666e3%2Ffo1w8d5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing and Confidence Interval Calculation for Two Populations
To solve these problems, follow the steps outlined below.
#### Assumptions:
- Both populations are normally distributed.
#### Given Data:
- **Sample 1**:
- \( n = 27 \)
- \( \overline{x} = 46.3 \)
- \( s = 9.1 \)
- **Sample 2**:
- \( n = 21 \)
- \( \overline{x} = 36.4 \)
- \( s = 8.7 \)
#### Tasks to Perform:
1. **Test whether \(\mu_1 > \mu_2\) at \(\alpha = 0.05\) level of significance for the given sample data.**
2. **Construct a 95% confidence interval about \(\mu_1 - \mu_2\).**
#### Procedure:
1. **Testing the Hypothesis: \( \mu_1 > \mu_2 \)**
**Hypotheses:**
- \( H_0: \mu_1 \leq \mu_2 \)
- \( H_1: \mu_1 > \mu_2 \)
2. **Determine the Test Statistic \( t \):**
\[
t = \text{(Round to two decimal places as needed.)}
\]
3. **Determine the Critical Value(s):**
- Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed).
- \( A. \) The critical value is
- \( B. \) The lower critical value is \_\_\_\_\_. The upper critical value is \_\_\_\_\_.
4. **Determine Whether the Hypothesis Should be Rejected:**
- Reject the null hypothesis because the test statistic \( \_\_\_\_\_\_\ ) the critical region.
### Constructing a 95% Confidence Interval for \( \mu_1 - \mu_2 \)
The confidence interval is the range from \[\_\_\_\_\_\_\_\] to \[\_\_\_\_\_\_\_\].
(Round to two decimal places as needed. Use ascending order.)
#### Graph Explanation:
There is an inserted window titled "Student t-Distribution Table" that shows critical t-values for various
![### Statistical Analysis Case Study
#### Assumptions
Assume that both populations are normally distributed.
### Tasks
a) **Hypothesis Test**
Test whether \( \mu_1 > \mu_2 \) at the \( \alpha = 0.05 \) level of significance for the given sample data.
b) **Confidence Interval**
Construct a 95% confidence interval about \( \mu_1 - \mu_2 \).
### Sample Data
| | Sample 1 | Sample 2 |
|---------|----------|----------|
| n | 27 | 21 |
| \(\bar{x}\) (mean) | 46.3 | 36.4 |
| s (standard deviation) | 9.1 | 8.7 |
### Instructions
1. Click the icon to view the Student t-distribution table. [Note: In an actual educational website this would be a clickable link or button]
### Step-by-Step Solution
#### a) Perform a Hypothesis Test
Determine the null and alternative hypotheses.
Options:
- **A.** \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 > \mu_2 \)
- **B.** \( H_0: \mu_1 \le \mu_2 \), \( H_1: \mu_1 > \mu_2 \)
- **C.** \( H_0: \mu_1 \ge \mu_2 \), \( H_1: \mu_1 < \mu_2 \)
- **D.** \( H_0: \mu_1 \ne \mu_2 \), \( H_1: \mu_1 = \mu_2 \)
Determine the test statistic:
\[ t = \boxed{\ } \text{ (Round to two decimal places as needed).} \]
Determine the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.)
- **A.** The critical value is \( \boxed{\ }\).
- **B.** The lower critical value is \( \boxed{\ }\) The upper critical value is \( \boxed{\ }\).
(Note: The actual computation was not completed in the image. Thus, students should refer to the appropriate statistical](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd86b4514-aa18-4e84-8d65-86fc6c642f07%2F26e9082a-570f-453f-90d9-ad1eb01666e3%2Fgx1kots_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis Case Study
#### Assumptions
Assume that both populations are normally distributed.
### Tasks
a) **Hypothesis Test**
Test whether \( \mu_1 > \mu_2 \) at the \( \alpha = 0.05 \) level of significance for the given sample data.
b) **Confidence Interval**
Construct a 95% confidence interval about \( \mu_1 - \mu_2 \).
### Sample Data
| | Sample 1 | Sample 2 |
|---------|----------|----------|
| n | 27 | 21 |
| \(\bar{x}\) (mean) | 46.3 | 36.4 |
| s (standard deviation) | 9.1 | 8.7 |
### Instructions
1. Click the icon to view the Student t-distribution table. [Note: In an actual educational website this would be a clickable link or button]
### Step-by-Step Solution
#### a) Perform a Hypothesis Test
Determine the null and alternative hypotheses.
Options:
- **A.** \( H_0: \mu_1 = \mu_2 \), \( H_1: \mu_1 > \mu_2 \)
- **B.** \( H_0: \mu_1 \le \mu_2 \), \( H_1: \mu_1 > \mu_2 \)
- **C.** \( H_0: \mu_1 \ge \mu_2 \), \( H_1: \mu_1 < \mu_2 \)
- **D.** \( H_0: \mu_1 \ne \mu_2 \), \( H_1: \mu_1 = \mu_2 \)
Determine the test statistic:
\[ t = \boxed{\ } \text{ (Round to two decimal places as needed).} \]
Determine the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.)
- **A.** The critical value is \( \boxed{\ }\).
- **B.** The lower critical value is \( \boxed{\ }\) The upper critical value is \( \boxed{\ }\).
(Note: The actual computation was not completed in the image. Thus, students should refer to the appropriate statistical
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