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2. Set up the sampling distribution. Select o Locate region of rejection Determine critical value

2. Set up the sampling distribution. Select o Locate region of rejection Determine critical value

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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### Setting Up the Sampling Distribution: 1. **Select α (alpha):** - The first step in setting up the sampling distribution involves selecting the significance level, denoted as α (alpha). This value determines the probability of rejecting the null hypothesis when it is actually true. Common values for α include 0.05, 0.01, and 0.10. 2. **Locate Region of Rejection:** - After selecting α, the next step is to locate the region of rejection on the distribution curve. This region corresponds to the extreme values of the sampling distribution where the null hypothesis is rejected. The area of this region is equal to the selected α value. 3. **Determine Critical Value:** - The critical value(s) is determined based on the chosen α. The critical value marks the boundary between the region where the null hypothesis is accepted and the region where it is rejected. This value is often found using statistical tables or software. ### Graph Explanation: - **Graph Description:** - The provided graph is a bell-shaped curve, representing a normal distribution. - The x-axis represents the sample values, and the y-axis represents the probability density. - The bell curve is symmetrical, with the highest point at the center representing the mean of the distribution. - **Steps Indicated on the Graph:** - **Select α:** The leftmost part of the text emphasizes choosing the level of significance. - **Locate Region of Rejection:** This is represented graphically by the shaded tails of the bell curve, signifying the area where the null hypothesis would be rejected. - **Determine Critical Value:** The critical values are the points on the x-axis at the edges of the shaded regions. These indicate the thresholds beyond which the results are considered statistically significant. Understanding these steps and the accompanying graph is crucial for setting up and interpreting a sampling distribution in hypothesis testing.
Transcribed Image Text:### Setting Up the Sampling Distribution: 1. **Select α (alpha):** - The first step in setting up the sampling distribution involves selecting the significance level, denoted as α (alpha). This value determines the probability of rejecting the null hypothesis when it is actually true. Common values for α include 0.05, 0.01, and 0.10. 2. **Locate Region of Rejection:** - After selecting α, the next step is to locate the region of rejection on the distribution curve. This region corresponds to the extreme values of the sampling distribution where the null hypothesis is rejected. The area of this region is equal to the selected α value. 3. **Determine Critical Value:** - The critical value(s) is determined based on the chosen α. The critical value marks the boundary between the region where the null hypothesis is accepted and the region where it is rejected. This value is often found using statistical tables or software. ### Graph Explanation: - **Graph Description:** - The provided graph is a bell-shaped curve, representing a normal distribution. - The x-axis represents the sample values, and the y-axis represents the probability density. - The bell curve is symmetrical, with the highest point at the center representing the mean of the distribution. - **Steps Indicated on the Graph:** - **Select α:** The leftmost part of the text emphasizes choosing the level of significance. - **Locate Region of Rejection:** This is represented graphically by the shaded tails of the bell curve, signifying the area where the null hypothesis would be rejected. - **Determine Critical Value:** The critical values are the points on the x-axis at the edges of the shaded regions. These indicate the thresholds beyond which the results are considered statistically significant. Understanding these steps and the accompanying graph is crucial for setting up and interpreting a sampling distribution in hypothesis testing.
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