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In 1995, it was determined that 78% of US citizens supported a ban on household aerosols.  Thinking that this proportion may have changed over the past few decades, a sample will be taken to test if a change has occurred. 1) What is the appropriate null hypothesis?  H0:  2) What is the appropriate alternative hypothesis?  Ha:

In 1995, it was determined that 78% of US citizens supported a ban on household aerosols.  Thinking that this proportion may have changed over the past few decades, a sample will be taken to test if a change has occurred. 1) What is the appropriate null hypothesis?  H0:  2) What is the appropriate alternative hypothesis?  Ha:

MATLAB: An Introduction with Applications
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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In 1995, it was determined that 78% of US citizens supported a ban on household aerosols.  Thinking that this proportion may have changed over the past few decades, a sample will be taken to test if a change has occurred.

1) What is the appropriate null hypothesis?  H0: 

2) What is the appropriate alternative hypothesis?  Ha: 

### Selecting the Appropriate Alternative Hypothesis In statistical hypothesis testing, an alternative hypothesis (denoted as Ha) is a statement that indicates the presence of an effect, relationship, or difference in a population parameter as opposed to the null hypothesis (H0) which assumes no effect or difference. The image presents a multiple-choice question designed to test your understanding of how to select an appropriate alternative hypothesis. Below is the information displayed on the image: #### Options for Alternative Hypothesis (Ha) - [ ] \( p < 0.78 \) - [ ] \( \mu > 78 \) - [ ] \( p > 0.78 \) - [ ] \( p \neq 0.78 \) - [ ] \( \mu < 78 \) - [ ] \( \mu \neq 78 \) #### Question: **What is the appropriate alternative hypothesis? Ha:** #### Explanation: 1. **Alternative Hypothesis**: It is a statement that implies a difference, effect, or relationship that contradicts the null hypothesis. Depending on what you are testing (proportion or mean) and the specifics of the research question or objective, the form of the alternative hypothesis will change. 2. **Symbols**: - \( p \): Indicates population proportion. - \( \mu \): Indicates population mean. 3. **Types of Tests**: - **One-tailed test**: Tests for a direction, either less than (<) or greater than (>) a certain value. - **Two-tailed test**: Tests for any difference, which can be either less than or greater than (≠) a certain value. ### Visualization Explanation: - The image lists six options for alternative hypotheses involving proportions (p) and means (μ). Only one of these options is correct depending on the context of the research or study being addressed. **Note:** To choose the correct alternative hypothesis, you must understand the context or aim of the statistical test being conducted. For example, if you are testing whether the mean of a data set is different from 78, you would choose \(\mu \neq 78\). ### Practical Usage: When faced with such multiple-choice questions, always refer back to the precise research question or objective you are studying to determine the correct form of the alternative hypothesis. Ensure that you understand whether a one-tailed or two-tailed test is appropriate based on the hypothesis testing scenario.
Transcribed Image Text:### Selecting the Appropriate Alternative Hypothesis In statistical hypothesis testing, an alternative hypothesis (denoted as Ha) is a statement that indicates the presence of an effect, relationship, or difference in a population parameter as opposed to the null hypothesis (H0) which assumes no effect or difference. The image presents a multiple-choice question designed to test your understanding of how to select an appropriate alternative hypothesis. Below is the information displayed on the image: #### Options for Alternative Hypothesis (Ha) - [ ] \( p < 0.78 \) - [ ] \( \mu > 78 \) - [ ] \( p > 0.78 \) - [ ] \( p \neq 0.78 \) - [ ] \( \mu < 78 \) - [ ] \( \mu \neq 78 \) #### Question: **What is the appropriate alternative hypothesis? Ha:** #### Explanation: 1. **Alternative Hypothesis**: It is a statement that implies a difference, effect, or relationship that contradicts the null hypothesis. Depending on what you are testing (proportion or mean) and the specifics of the research question or objective, the form of the alternative hypothesis will change. 2. **Symbols**: - \( p \): Indicates population proportion. - \( \mu \): Indicates population mean. 3. **Types of Tests**: - **One-tailed test**: Tests for a direction, either less than (<) or greater than (>) a certain value. - **Two-tailed test**: Tests for any difference, which can be either less than or greater than (≠) a certain value. ### Visualization Explanation: - The image lists six options for alternative hypotheses involving proportions (p) and means (μ). Only one of these options is correct depending on the context of the research or study being addressed. **Note:** To choose the correct alternative hypothesis, you must understand the context or aim of the statistical test being conducted. For example, if you are testing whether the mean of a data set is different from 78, you would choose \(\mu \neq 78\). ### Practical Usage: When faced with such multiple-choice questions, always refer back to the precise research question or objective you are studying to determine the correct form of the alternative hypothesis. Ensure that you understand whether a one-tailed or two-tailed test is appropriate based on the hypothesis testing scenario.
**Choosing the Appropriate Null Hypothesis** In statistical hypothesis testing, selecting the correct null hypothesis (H0) is essential for accurately interpreting the results of an experiment. The null hypothesis generally represents the default position that there is no effect or no difference. **Question: What is the appropriate null hypothesis? H0:** **Options:** 1. \( p \neq 0.78 \) 2. \( p = 0.78 \) 3. \( \mu \neq 78 \) 4. \( \mu = 78 \) **Explanation:** - **\( p \neq 0.78 \)**: This suggests that the proportion is not equal to 0.78. It is an example of an alternative hypothesis rather than a null hypothesis. - **\( p = 0.78 \)**: This indicates that the proportion is equal to 0.78. This is a typical null hypothesis format. - **\( \mu \neq 78 \)**: This implies that the mean is not equal to 78 and represents an alternative hypothesis. - **\( \mu = 78 \)**: This states that the mean is equal to 78 and is a correct form of a null hypothesis. **In conclusion, the appropriate null hypothesis (H0) would typically be expressed as equality. For this question, the proper null hypotheses are either \( p = 0.78 \) or \( \mu = 78 \), depending on what parameter we are focusing on.**
Transcribed Image Text:**Choosing the Appropriate Null Hypothesis** In statistical hypothesis testing, selecting the correct null hypothesis (H0) is essential for accurately interpreting the results of an experiment. The null hypothesis generally represents the default position that there is no effect or no difference. **Question: What is the appropriate null hypothesis? H0:** **Options:** 1. \( p \neq 0.78 \) 2. \( p = 0.78 \) 3. \( \mu \neq 78 \) 4. \( \mu = 78 \) **Explanation:** - **\( p \neq 0.78 \)**: This suggests that the proportion is not equal to 0.78. It is an example of an alternative hypothesis rather than a null hypothesis. - **\( p = 0.78 \)**: This indicates that the proportion is equal to 0.78. This is a typical null hypothesis format. - **\( \mu \neq 78 \)**: This implies that the mean is not equal to 78 and represents an alternative hypothesis. - **\( \mu = 78 \)**: This states that the mean is equal to 78 and is a correct form of a null hypothesis. **In conclusion, the appropriate null hypothesis (H0) would typically be expressed as equality. For this question, the proper null hypotheses are either \( p = 0.78 \) or \( \mu = 78 \), depending on what parameter we are focusing on.**
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