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)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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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.

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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