Compute the power of the test if the researcher uses a sample of n = 4 individuals. The power for the test is the probability of obtaining a z-score than , which corresponds to p = Thus, the power of the test is %. Compute the power of the test if the researcher uses a sample of n = 25 individuals. The power for the test is the probability of obtaining a z-score than which corresponds to p = Thus, the %3D power of the test is 이0.

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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.
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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