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Match each P-value with the graph that displays its area without performing any calculations. Explain your reasoning. P= 0.0125 and P= 0.2296. (a) z= - 2.24 (b) z = - 0.74 ..... Graph V displays the area for P = 0.0125 and graph V displays the area for P = 0.2296 because the P-value V the shaded area. absolute value of z.

Match each P-value with the graph that displays its area without performing any calculations. Explain your reasoning. P= 0.0125 and P= 0.2296. (a) z= - 2.24 (b) z = - 0.74 ..... Graph V displays the area for P = 0.0125 and graph V displays the area for P = 0.2296 because the P-value V the shaded area. absolute value of z.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The image displays a multiple-choice exercise involving normal distribution graphs and P-values: ### Problem Statement: Match each P-value with the graph that displays its area without performing any calculations. Explain your reasoning. - Given P-values: \( P = 0.0125 \) and \( P = 0.2296 \). ### Graph Descriptions: 1. **Graph (a):** - Shows a normal distribution curve with a marked Z-score of \( z = -2.24 \). - The area under the curve to the left of this Z-score is shaded. 2. **Graph (b):** - Displays another normal distribution curve with a marked Z-score of \( z = -0.74 \). - The area under the curve to the left of this Z-score is shaded. ### Task: - Using dropdown menus: - Select which graph displays the area for \( P = 0.0125 \). - Select which graph displays the area for \( P = 0.2296 \). ### Explanation Prompt: - Complete the statement explaining the relationship between the graphs and P-values: "Graph __ displays the area for \( P = 0.0125 \) and graph __ displays the area for \( P = 0.2296 \) because the P-value __ the __." ### Multiple Choice Options: - Is equal to one minus - Is equal to - Is related to - Is related to one minus ### Interface Options: - "Help me solve this" - "View an example" - "Get more help" - Buttons for "Clear all" and "Check answer" This exercise helps understand how Z-scores correspond to areas under the normal distribution curve related to specific P-values.
Transcribed Image Text:The image displays a multiple-choice exercise involving normal distribution graphs and P-values: ### Problem Statement: Match each P-value with the graph that displays its area without performing any calculations. Explain your reasoning. - Given P-values: \( P = 0.0125 \) and \( P = 0.2296 \). ### Graph Descriptions: 1. **Graph (a):** - Shows a normal distribution curve with a marked Z-score of \( z = -2.24 \). - The area under the curve to the left of this Z-score is shaded. 2. **Graph (b):** - Displays another normal distribution curve with a marked Z-score of \( z = -0.74 \). - The area under the curve to the left of this Z-score is shaded. ### Task: - Using dropdown menus: - Select which graph displays the area for \( P = 0.0125 \). - Select which graph displays the area for \( P = 0.2296 \). ### Explanation Prompt: - Complete the statement explaining the relationship between the graphs and P-values: "Graph __ displays the area for \( P = 0.0125 \) and graph __ displays the area for \( P = 0.2296 \) because the P-value __ the __." ### Multiple Choice Options: - Is equal to one minus - Is equal to - Is related to - Is related to one minus ### Interface Options: - "Help me solve this" - "View an example" - "Get more help" - Buttons for "Clear all" and "Check answer" This exercise helps understand how Z-scores correspond to areas under the normal distribution curve related to specific P-values.
### Understanding P-Values and Their Graphical Representations #### Overview: This tool helps you match P-values with corresponding graphs that depict their areas on a standard normal distribution curve. The task is to do so without calculating the P-values manually. The given P-values are 0.0125 and 0.2296. #### Graph Details: 1. **Graph (a):** - **Z-score:** -2.24 - **Description:** This graph shows a normal distribution curve with the area to the left of the z-score (-2.24) shaded. This shaded area represents the P-value, which is a measure of the probability of observing a value as extreme as the test statistic under the null hypothesis. 2. **Graph (b):** - **Z-score:** -0.74 - **Description:** This graph illustrates a normal distribution with the area to the left of the z-score (-0.74) shaded. As with the previous graph, the shaded area corresponds to the P-value. #### Matching P-values with Graphs: - **Graph Selection:** - For a P-value of 0.0125, select the graph where the left-shaded area is relatively small, as this indicates a smaller probability. - For a P-value of 0.2296, select the graph where the left-shaded area is larger, reflecting a higher probability. #### Dropdown Explanation: - A dropdown menu allows you to choose the graph that displays each P-value by visual comparison of the shaded areas relative to the standard normal curve. - The option to match based on "absolute value of z" is available, indicating that one can consider z-scores when determining which graph represents a particular P-value. #### Interactive Features: - **Additional Options:** - "Help me solve this" can guide step-by-step through the process. - "View an example" provides a practical demonstration of similar problems. - "Get more help" offers further resources or support. This educational task enhances understanding of standard normal distributions and the interpretation of P-values in statistical analysis.
Transcribed Image Text:### Understanding P-Values and Their Graphical Representations #### Overview: This tool helps you match P-values with corresponding graphs that depict their areas on a standard normal distribution curve. The task is to do so without calculating the P-values manually. The given P-values are 0.0125 and 0.2296. #### Graph Details: 1. **Graph (a):** - **Z-score:** -2.24 - **Description:** This graph shows a normal distribution curve with the area to the left of the z-score (-2.24) shaded. This shaded area represents the P-value, which is a measure of the probability of observing a value as extreme as the test statistic under the null hypothesis. 2. **Graph (b):** - **Z-score:** -0.74 - **Description:** This graph illustrates a normal distribution with the area to the left of the z-score (-0.74) shaded. As with the previous graph, the shaded area corresponds to the P-value. #### Matching P-values with Graphs: - **Graph Selection:** - For a P-value of 0.0125, select the graph where the left-shaded area is relatively small, as this indicates a smaller probability. - For a P-value of 0.2296, select the graph where the left-shaded area is larger, reflecting a higher probability. #### Dropdown Explanation: - A dropdown menu allows you to choose the graph that displays each P-value by visual comparison of the shaded areas relative to the standard normal curve. - The option to match based on "absolute value of z" is available, indicating that one can consider z-scores when determining which graph represents a particular P-value. #### Interactive Features: - **Additional Options:** - "Help me solve this" can guide step-by-step through the process. - "View an example" provides a practical demonstration of similar problems. - "Get more help" offers further resources or support. This educational task enhances understanding of standard normal distributions and the interpretation of P-values in statistical analysis.
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