MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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The image illustrates a right tail test on a normal distribution curve where the null hypothesis is not rejected. Below the graph are terms that need to be matched to specific points on the curve.

### Graph Explanation:

- **Normal Distribution Curve**: The blue curve represents the normal distribution.
- **Null Hypothesis Value (a)**: Labeled as "a", this point is at the center of the curve, representing the mean under the null hypothesis.
- **P-value (b)**: Labeled as "b", this point is further to the right on the horizontal axis within the shaded area, representing the P-value region.
- **Significance Level (c)**: Labeled as "c", this point, marked in red, lies very close to "d", within the shaded tail area.
- **Test Statistic (d)**: Labeled as "d", this is the point marking the boundary of the test statistic's distribution, located just at the edge of the shaded region.
- **Critical Value (e)**: Labeled as "e", it is positioned at the beginning of the shaded section marking the boundary for rejection.

### Label Explanation:

- **Significance Level**: Represents the threshold at which the test determines statistical significance; located at point "c".
- **Null Hypothesis Value**: The hypothesized average value, shown at point "a".
- **Test Statistic**: The computed value from the sample data, labeled as "d".
- **P-value**: Probability of observing a test statistic as extreme as, or more extreme than, the one observed; marked as "b".
- **Critical Value**: The threshold beyond which the null hypothesis is rejected; located at "e".

This setup visually explains the concepts involved in hypothesis testing on a normal distribution, showing where and why the null hypothesis remains accepted due to the arrangement of the values.
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Transcribed Image Text:The image illustrates a right tail test on a normal distribution curve where the null hypothesis is not rejected. Below the graph are terms that need to be matched to specific points on the curve. ### Graph Explanation: - **Normal Distribution Curve**: The blue curve represents the normal distribution. - **Null Hypothesis Value (a)**: Labeled as "a", this point is at the center of the curve, representing the mean under the null hypothesis. - **P-value (b)**: Labeled as "b", this point is further to the right on the horizontal axis within the shaded area, representing the P-value region. - **Significance Level (c)**: Labeled as "c", this point, marked in red, lies very close to "d", within the shaded tail area. - **Test Statistic (d)**: Labeled as "d", this is the point marking the boundary of the test statistic's distribution, located just at the edge of the shaded region. - **Critical Value (e)**: Labeled as "e", it is positioned at the beginning of the shaded section marking the boundary for rejection. ### Label Explanation: - **Significance Level**: Represents the threshold at which the test determines statistical significance; located at point "c". - **Null Hypothesis Value**: The hypothesized average value, shown at point "a". - **Test Statistic**: The computed value from the sample data, labeled as "d". - **P-value**: Probability of observing a test statistic as extreme as, or more extreme than, the one observed; marked as "b". - **Critical Value**: The threshold beyond which the null hypothesis is rejected; located at "e". This setup visually explains the concepts involved in hypothesis testing on a normal distribution, showing where and why the null hypothesis remains accepted due to the arrangement of the values.
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