Treatment Placebo A study was done 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 0.10 significance level for both parts. 27 39 In 2.39 0.94 2.64 0.62 populations with the same mean. OD. Fall to reject the null hypothesis. There is sufficlent evidence to warrant rejection of the claim that the two samples are from populations with the same mean. b. Construct a confidence interval suitable for testing the daim that the two samples are from populations with the same mean. (Round to three decimal places as needed.)
Treatment Placebo A study was done 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 0.10 significance level for both parts. 27 39 In 2.39 0.94 2.64 0.62 populations with the same mean. OD. Fall to reject the null hypothesis. There is sufficlent evidence to warrant rejection of the claim that the two samples are from populations with the same mean. b. Construct a confidence interval suitable for testing the daim that the two samples are from populations with the same mean. (Round to three decimal places as needed.)
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 3 ( B )
![**Study Analysis Using Treatment and Placebo Groups**
A study was conducted employing a treatment group and a placebo group. The results are detailed in the table provided. The assumptions are as follows: the two samples are independent simple random samples drawn from normally distributed populations. It is also assumed that the population standard deviations are not equal. The following parts (a) and (b) must be completed using a significance level of 0.10.
**Data Table:**
| | Treatment | Placebo |
|----------------|-----------|---------|
| Sample Size (\(n\)) | 27 | 39 |
| Mean (\(\bar{x}\)) | 2.39 | 2.64 |
| Standard Deviation (\(s\)) | 0.94 | 0.62 |
**Tasks:**
**a. Hypothesis Test:**
1. **Null Hypothesis (\(H_0\))**: The two samples are from populations with the same mean.
2. Evaluate the evidence and choose one:
- Fail to reject the null hypothesis.
- Reject the null hypothesis.
**b. Confidence Interval:**
Construct a confidence interval that is suitable for testing the claim that the two samples come from populations with the same mean.
**Hypothesis Notation:**
\[
H_0: \mu_1 = \mu_2
\]
\[
H_1: \mu_1 \neq \mu_2
\]
*(Note: Round answers to three decimal places when necessary.)*
This form of analysis is crucial in determining whether the treatment has a statistically significant effect compared to the placebo, based on the measured parameters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb153809b-6548-4767-944e-20bfb299f2a4%2F33e54e34-a14c-456e-af32-f3909e7ca2b4%2Fboecvac_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Study Analysis Using Treatment and Placebo Groups**
A study was conducted employing a treatment group and a placebo group. The results are detailed in the table provided. The assumptions are as follows: the two samples are independent simple random samples drawn from normally distributed populations. It is also assumed that the population standard deviations are not equal. The following parts (a) and (b) must be completed using a significance level of 0.10.
**Data Table:**
| | Treatment | Placebo |
|----------------|-----------|---------|
| Sample Size (\(n\)) | 27 | 39 |
| Mean (\(\bar{x}\)) | 2.39 | 2.64 |
| Standard Deviation (\(s\)) | 0.94 | 0.62 |
**Tasks:**
**a. Hypothesis Test:**
1. **Null Hypothesis (\(H_0\))**: The two samples are from populations with the same mean.
2. Evaluate the evidence and choose one:
- Fail to reject the null hypothesis.
- Reject the null hypothesis.
**b. Confidence Interval:**
Construct a confidence interval that is suitable for testing the claim that the two samples come from populations with the same mean.
**Hypothesis Notation:**
\[
H_0: \mu_1 = \mu_2
\]
\[
H_1: \mu_1 \neq \mu_2
\]
*(Note: Round answers to three decimal places when necessary.)*
This form of analysis is crucial in determining whether the treatment has a statistically significant effect compared to the placebo, based on the measured parameters.
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