Find the T and P value
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
Find the T and P value
![A study was conducted using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts.
**Table:**
- **Treatment Group:**
- Sample size (n): 26
- Mean (\(\bar{x}\)): 2.32
- Standard deviation (s): 0.61
- **Placebo Group:**
- Sample size (n): 34
- Mean (\(\bar{x}\)): 2.66
- Standard deviation (s): 0.99
**a. Test the claim that the two samples are from populations with the same mean.**
**What are the null and alternative hypotheses?**
- Option A:
- Null Hypothesis (\(H_0\)): \(\mu_1 = \mu_2\)
- Alternative Hypothesis (\(H_1\)): \(\mu_1 \neq \mu_2\)
- Option B:
- Null Hypothesis (\(H_0\)): \(\mu_1 \neq \mu_2\)
- Alternative Hypothesis (\(H_1\)): \(\mu_1 < \mu_2\)
- Option C:
- Null Hypothesis (\(H_0\)): \(\mu_1 < \mu_2\)
- Alternative Hypothesis (\(H_1\)): \(\mu_1 \geq \mu_2\)
- Option D:
- Null Hypothesis (\(H_0\)): \(\mu_1 = \mu_2\)
- Alternative Hypothesis (\(H_1\)): \(\mu_1 > \mu_2\)
**The test statistic, \(t\), is [ ]** (Round to two decimal places as needed.)
**Instructions:**
Enter your answer in the answer box and then click "Check Answer".
**Note:** There are 3 parts remaining to complete this task.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2734b2e5-bfdc-4698-b164-7fb7c5253f73%2F1540944d-9671-4e50-8de7-1be74756c806%2Fx9wcg19_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A study was conducted using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts.
**Table:**
- **Treatment Group:**
- Sample size (n): 26
- Mean (\(\bar{x}\)): 2.32
- Standard deviation (s): 0.61
- **Placebo Group:**
- Sample size (n): 34
- Mean (\(\bar{x}\)): 2.66
- Standard deviation (s): 0.99
**a. Test the claim that the two samples are from populations with the same mean.**
**What are the null and alternative hypotheses?**
- Option A:
- Null Hypothesis (\(H_0\)): \(\mu_1 = \mu_2\)
- Alternative Hypothesis (\(H_1\)): \(\mu_1 \neq \mu_2\)
- Option B:
- Null Hypothesis (\(H_0\)): \(\mu_1 \neq \mu_2\)
- Alternative Hypothesis (\(H_1\)): \(\mu_1 < \mu_2\)
- Option C:
- Null Hypothesis (\(H_0\)): \(\mu_1 < \mu_2\)
- Alternative Hypothesis (\(H_1\)): \(\mu_1 \geq \mu_2\)
- Option D:
- Null Hypothesis (\(H_0\)): \(\mu_1 = \mu_2\)
- Alternative Hypothesis (\(H_1\)): \(\mu_1 > \mu_2\)
**The test statistic, \(t\), is [ ]** (Round to two decimal places as needed.)
**Instructions:**
Enter your answer in the answer box and then click "Check Answer".
**Note:** There are 3 parts remaining to complete this task.
Expert Solution
Step 1
Study was done using a treatment group and placebo group.
Results are:
|
|
Treatment |
Placebo |
|
µ |
µ1 |
µ2 |
|
n |
n1=26 |
n2=34 |
|
x̅ |
x̅1=2.32 |
x̅2=2.66 |
|
s |
s1=0.61 |
s2=0.99 |
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