MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![### Hypothesis Testing Using t-Distribution
In this example, we aim to test the following hypotheses:
- Null Hypothesis (H₀): μ = 20
- Alternative Hypothesis (H₁): μ < 20
A simple random sample of size n = 19 is obtained from a population that is known to be normally distributed. We will address the following parts (a)- (d):
1. **Click here to view the t-Distribution Area in Right Tail.**
2. **Part (a)**
If the sample mean (x̄) is 18.4 and the sample standard deviation (s) is 4.3, compute the test statistic using the formula for a one-sample t-test:
\[
t = \frac{\overline{x} - \mu}{s / \sqrt{n}}
\]
- Here, \(\overline{x} = 18.4\)
- \(\mu = 20\)
- \(s = 4.3\)
- \(n = 19\)
Compute the t value (Round to two decimal places as needed):
(formula and calculation steps to be shown)
### Interactive Features
- **Help me solve this**: Provides step-by-step guidance to solve the problem.
- **View an example**: Shows how to work through a similar problem with different data.
- **Get more help**: Additional resources or access to a tutor or instructor.
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### Current Status Indicators
- **94°F** | Mostly sunny
- **Date and Time**: 1:14 PM, 6/18/2022
By working through this example, students will learn how to perform hypothesis testing for the mean using the t-distribution and how to interpret the calculated test statistic in the context of the given hypotheses.](https://content.bartleby.com/qna-images/question/2241529c-3605-4343-8b09-279b4f80df33/57d0b23a-4b07-47ec-a8ca-4e21e34bcf96/fh1l5a_processed.jpeg)
Transcribed Image Text:### Hypothesis Testing Using t-Distribution
In this example, we aim to test the following hypotheses:
- Null Hypothesis (H₀): μ = 20
- Alternative Hypothesis (H₁): μ < 20
A simple random sample of size n = 19 is obtained from a population that is known to be normally distributed. We will address the following parts (a)- (d):
1. **Click here to view the t-Distribution Area in Right Tail.**
2. **Part (a)**
If the sample mean (x̄) is 18.4 and the sample standard deviation (s) is 4.3, compute the test statistic using the formula for a one-sample t-test:
\[
t = \frac{\overline{x} - \mu}{s / \sqrt{n}}
\]
- Here, \(\overline{x} = 18.4\)
- \(\mu = 20\)
- \(s = 4.3\)
- \(n = 19\)
Compute the t value (Round to two decimal places as needed):
(formula and calculation steps to be shown)
### Interactive Features
- **Help me solve this**: Provides step-by-step guidance to solve the problem.
- **View an example**: Shows how to work through a similar problem with different data.
- **Get more help**: Additional resources or access to a tutor or instructor.
- **Clear all**: Clears any input or selections made.
- **Check answer**: Validates the inputted answer against the correct one.
### Current Status Indicators
- **94°F** | Mostly sunny
- **Date and Time**: 1:14 PM, 6/18/2022
By working through this example, students will learn how to perform hypothesis testing for the mean using the t-distribution and how to interpret the calculated test statistic in the context of the given hypotheses.
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