19) Do a hypothesis for the following, make sure to include and label all five steps: Test the claim that Treatment is independent of your reaction. Use a .05 significance level. Drug Placebo Headaches 18 20 No Headaches 82 70
19) Do a hypothesis for the following, make sure to include and label all five steps: Test the claim that Treatment is independent of your reaction. Use a .05 significance level. Drug Placebo Headaches 18 20 No Headaches 82 70
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
Concept explainers
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
Topic Video
Question
Can I get some help with #19??
![### Hypothesis Testing: Treatment Independence
#### Problem Statement
**Question:**
Do a hypothesis for the following. Make sure to include and label all five steps. Test the claim that treatment is independent of your reaction. Use a 0.05 significance level.
#### Data Table
The table below provides the frequency of headaches and no headaches among two groups: one receiving a drug and the other receiving a placebo.
| Reaction | Drug | Placebo |
|---------------|------|---------|
| Headaches | 18 | 20 |
| No Headaches | 82 | 70 |
#### Explanation of the Data Table
- **Headaches (Drug)**: Number of people who developed headaches after receiving the drug (18 individuals).
- **Headaches (Placebo)**: Number of people who developed headaches after receiving the placebo (20 individuals).
- **No Headaches (Drug)**: Number of people who did not develop headaches after receiving the drug (82 individuals).
- **No Headaches (Placebo)**: Number of people who did not develop headaches after receiving the placebo (70 individuals).
#### Hypothesis Testing Steps
1. **State the Hypotheses:**
- Null Hypothesis (\(H_0\)): Treatment (Drug or Placebo) is independent of the occurrence of headaches.
- Alternative Hypothesis (\(H_1\)): Treatment (Drug or Placebo) is not independent of the occurrence of headaches.
2. **Significance Level (\(\alpha\)):**
- The significance level is set at 0.05.
3. **Test Statistic:**
- Calculate the chi-square test statistic for the given data.
4. **Decision Rule:**
- Determine the critical value from the chi-square distribution table with the appropriate degrees of freedom (df).
- Degrees of freedom (df) can be calculated as:
\[
df = (r-1) \cdot (c-1)
\]
where \(r\) is the number of rows and \(c\) is the number of columns. For this table, \(df = (2-1) \cdot (2-1) = 1\).
5. **Conclusion:**
- Compare the calculated chi-square test statistic to the critical value.
- Reject \(H_0\) if the test statistic is greater than the critical value; otherwise, do](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6ad1cd7-e883-4155-acb4-5513247aaa08%2Fa8b0548d-e441-4fbc-baa0-3bdb7e5a6440%2Feizmxe8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hypothesis Testing: Treatment Independence
#### Problem Statement
**Question:**
Do a hypothesis for the following. Make sure to include and label all five steps. Test the claim that treatment is independent of your reaction. Use a 0.05 significance level.
#### Data Table
The table below provides the frequency of headaches and no headaches among two groups: one receiving a drug and the other receiving a placebo.
| Reaction | Drug | Placebo |
|---------------|------|---------|
| Headaches | 18 | 20 |
| No Headaches | 82 | 70 |
#### Explanation of the Data Table
- **Headaches (Drug)**: Number of people who developed headaches after receiving the drug (18 individuals).
- **Headaches (Placebo)**: Number of people who developed headaches after receiving the placebo (20 individuals).
- **No Headaches (Drug)**: Number of people who did not develop headaches after receiving the drug (82 individuals).
- **No Headaches (Placebo)**: Number of people who did not develop headaches after receiving the placebo (70 individuals).
#### Hypothesis Testing Steps
1. **State the Hypotheses:**
- Null Hypothesis (\(H_0\)): Treatment (Drug or Placebo) is independent of the occurrence of headaches.
- Alternative Hypothesis (\(H_1\)): Treatment (Drug or Placebo) is not independent of the occurrence of headaches.
2. **Significance Level (\(\alpha\)):**
- The significance level is set at 0.05.
3. **Test Statistic:**
- Calculate the chi-square test statistic for the given data.
4. **Decision Rule:**
- Determine the critical value from the chi-square distribution table with the appropriate degrees of freedom (df).
- Degrees of freedom (df) can be calculated as:
\[
df = (r-1) \cdot (c-1)
\]
where \(r\) is the number of rows and \(c\) is the number of columns. For this table, \(df = (2-1) \cdot (2-1) = 1\).
5. **Conclusion:**
- Compare the calculated chi-square test statistic to the critical value.
- Reject \(H_0\) if the test statistic is greater than the critical value; otherwise, do
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 6 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman