MATLAB: An Introduction with Applications
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### Evaluating the Influence of a Treatment using Normally Distributed Populations
**Context**
A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with:
- Mean (μ) = 50
- Standard Deviation (σ) = 10
The researcher expects a +5-point treatment effect and plans to use a two-tailed hypothesis test with a significance level (α) of 0.05.
**Graph Explanation**
The image includes a Standard Normal Distribution graph, showcasing a bell curve centered at a mean of 0.0 with a standard deviation of 1.0. The distribution is divided into two halves at the mean:
- The left side of the curve (shaded in blue) represents the lower half, with an area of 0.5000.
- The right side of the curve (shaded in brown) represents the upper half, also with an area of 0.5000.
**Steps to Compute the Power of the Test:**
1. **Computing the power of the test for n = 4 individuals:**
- The power for the test is the probability of obtaining a z-score [greater/less] than [z-value], which corresponds to p = [p-value].
- Thus, the power of the test is [percentage]%.
2. **Computing the power of the test for n = 25 individuals:**
- The power for the test is the probability of obtaining a z-score [greater/less] than [z-value], which corresponds to p = [p-value].
- Thus, the power of the test is [percentage]%.
**Interactive Component**
Students can dynamically control the z-value and see corresponding changes in p-value, enhancing their understanding of statistical power within hypothesis testing.
---
**Note:** Be sure to include actual z-values and p-values based on the specific analysis and computations performed.](https://content.bartleby.com/qna-images/question/7c57c96f-026c-4ae6-b9e7-3f888aaa330f/f4c2df8f-71d4-4d65-ab68-7f8eec2e8316/0jwzyll.jpeg)
Transcribed Image Text:---
### Evaluating the Influence of a Treatment using Normally Distributed Populations
**Context**
A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with:
- Mean (μ) = 50
- Standard Deviation (σ) = 10
The researcher expects a +5-point treatment effect and plans to use a two-tailed hypothesis test with a significance level (α) of 0.05.
**Graph Explanation**
The image includes a Standard Normal Distribution graph, showcasing a bell curve centered at a mean of 0.0 with a standard deviation of 1.0. The distribution is divided into two halves at the mean:
- The left side of the curve (shaded in blue) represents the lower half, with an area of 0.5000.
- The right side of the curve (shaded in brown) represents the upper half, also with an area of 0.5000.
**Steps to Compute the Power of the Test:**
1. **Computing the power of the test for n = 4 individuals:**
- The power for the test is the probability of obtaining a z-score [greater/less] than [z-value], which corresponds to p = [p-value].
- Thus, the power of the test is [percentage]%.
2. **Computing the power of the test for n = 25 individuals:**
- The power for the test is the probability of obtaining a z-score [greater/less] than [z-value], which corresponds to p = [p-value].
- Thus, the power of the test is [percentage]%.
**Interactive Component**
Students can dynamically control the z-value and see corresponding changes in p-value, enhancing their understanding of statistical power within hypothesis testing.
---
**Note:** Be sure to include actual z-values and p-values based on the specific analysis and computations performed.
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