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0. Do not reject H0 Reject HO 07 0.4 0.3 10.01 2.326 413 -1.77 -0.59 0 059 1.77 2.95 O 2.326

0. Do not reject H0 Reject HO 07 0.4 0.3 10.01 2.326 413 -1.77 -0.59 0 059 1.77 2.95 O 2.326

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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The graph portrays the decision criterion for a hypothesis test for a population mean. The null hypothesis is Ho: u = u0. The curve is the normal curve for the test statistic under the assumption that the null hypothesis is true. A graphical display of the decision criterion follows. Determine the rejection region. Graph is attached.

### Understanding Hypothesis Testing with Z-Scores #### Graph Explanation: The graph displayed is a standard normal distribution curve, which is symmetric and bell-shaped. It represents the distribution of z-scores, which are standardized scores that indicate how many standard deviations an element is from the mean. - **Horizontal Axis (x-axis)**: This axis represents the z-scores, ranging approximately from -4.13 to 4.13. - **Vertical Axis (y-axis)**: This axis represents the probability density. Higher points indicate a greater likelihood of occurrences around the mean. - **Central Region (Do not reject H0)**: The majority of the curve falls in this region, signifying that data points within this area do not provide strong evidence against the null hypothesis \( H_0 \). This means that z-scores falling here are considered within the normal range. - **Right Tail (Reject H0)**: This region is shaded or marked off to the right of z = 2.326. It signifies that if a z-score falls in this area, it is statistically significant, and the null hypothesis \( H_0 \) should be rejected. This region is typically associated with a very low probability (p < 0.05), indicating rare or extreme outcomes. #### Key Points to Note: - **Z = 2.326**: This critical value marks the threshold for rejecting the null hypothesis. If the z-score is greater than 2.326, it falls in the "Reject H0" region. - **P-value = 0.01**: The area to the right of z = 2.326 represents a tail probability of 0.01, meaning there is a 1% chance that a value would lie in this extreme region if the null hypothesis were true. #### Multiple Choice Questions: 1. **2.326** 2. **All z-scores that lie to the right of 2.326** 3. **All z-scores that lie to the left of 2.326** The multiple-choice questions seem to assess understanding of the critical value and the regions for rejecting or not rejecting the null hypothesis: - The correct choice related to the rejection region is likely "**All z-scores that lie to the right of 2.326**" because this is where the graph indicates the null hypothesis should be rejected. This visual and textual explanation should help students grasp the key concepts of hypothesis testing using z-scores,
Transcribed Image Text:### Understanding Hypothesis Testing with Z-Scores #### Graph Explanation: The graph displayed is a standard normal distribution curve, which is symmetric and bell-shaped. It represents the distribution of z-scores, which are standardized scores that indicate how many standard deviations an element is from the mean. - **Horizontal Axis (x-axis)**: This axis represents the z-scores, ranging approximately from -4.13 to 4.13. - **Vertical Axis (y-axis)**: This axis represents the probability density. Higher points indicate a greater likelihood of occurrences around the mean. - **Central Region (Do not reject H0)**: The majority of the curve falls in this region, signifying that data points within this area do not provide strong evidence against the null hypothesis \( H_0 \). This means that z-scores falling here are considered within the normal range. - **Right Tail (Reject H0)**: This region is shaded or marked off to the right of z = 2.326. It signifies that if a z-score falls in this area, it is statistically significant, and the null hypothesis \( H_0 \) should be rejected. This region is typically associated with a very low probability (p < 0.05), indicating rare or extreme outcomes. #### Key Points to Note: - **Z = 2.326**: This critical value marks the threshold for rejecting the null hypothesis. If the z-score is greater than 2.326, it falls in the "Reject H0" region. - **P-value = 0.01**: The area to the right of z = 2.326 represents a tail probability of 0.01, meaning there is a 1% chance that a value would lie in this extreme region if the null hypothesis were true. #### Multiple Choice Questions: 1. **2.326** 2. **All z-scores that lie to the right of 2.326** 3. **All z-scores that lie to the left of 2.326** The multiple-choice questions seem to assess understanding of the critical value and the regions for rejecting or not rejecting the null hypothesis: - The correct choice related to the rejection region is likely "**All z-scores that lie to the right of 2.326**" because this is where the graph indicates the null hypothesis should be rejected. This visual and textual explanation should help students grasp the key concepts of hypothesis testing using z-scores,
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