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Match each P-value with the graph that displays its area without performing any calculations. Explain your reasoning. P=0.0150 and P=0.2776.

Match each P-value with the graph that displays its area without performing any calculations. Explain your reasoning. P=0.0150 and P=0.2776.

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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Question

Match each P-value with the graph that displays its area without performing any calculations. Explain your reasoning. P=0.0150 and P=0.2776.

**Educational Website Content: Understanding P-Values and Z-Scores** In this exercise, you will match each P-value with its corresponding graph based on the shaded area and given z-scores, without performing calculations. ### Task: Match each P-value with the graph that displays its corresponding area. Explain your reasoning using the given P-values: **P = 0.0150** and **P = 0.2776**. ### Graphs Overview: 1. **Graph (a)**: - **Z-Score:** \( z = -2.17 \) - **Description:** The graph shows a normal distribution curve with a peak at \( z = 0 \). The left tail is shaded, indicating the area for a negative z-score. 2. **Graph (b)**: - **Z-Score:** \( z = -0.59 \) - **Description:** Similarly, this graph depicts a normal distribution with shading in the left region where \( z = -0.59 \). The area is more pronounced compared to graph (a). ### Selection: - **Graph Selection:** - Identify which graph corresponds to each P-value. - Consider that a smaller P-value corresponds to a smaller shaded area under the curve. #### Options: - **Graph (a)** likely represents P = 0.0150 due to its smaller shaded area from the more extreme z-score of \(-2.17\). - **Graph (b)** likely represents P = 0.2776 with a larger shaded region closer to zero at \( z = -0.59 \). **Conclusion:** Understanding the concept behind P-values and normal distributions helps to interpret statistical data effectively. By analyzing the area under the curve for different z-scores, you can determine which graph corresponds to the given P-values without computation.
Transcribed Image Text:**Educational Website Content: Understanding P-Values and Z-Scores** In this exercise, you will match each P-value with its corresponding graph based on the shaded area and given z-scores, without performing calculations. ### Task: Match each P-value with the graph that displays its corresponding area. Explain your reasoning using the given P-values: **P = 0.0150** and **P = 0.2776**. ### Graphs Overview: 1. **Graph (a)**: - **Z-Score:** \( z = -2.17 \) - **Description:** The graph shows a normal distribution curve with a peak at \( z = 0 \). The left tail is shaded, indicating the area for a negative z-score. 2. **Graph (b)**: - **Z-Score:** \( z = -0.59 \) - **Description:** Similarly, this graph depicts a normal distribution with shading in the left region where \( z = -0.59 \). The area is more pronounced compared to graph (a). ### Selection: - **Graph Selection:** - Identify which graph corresponds to each P-value. - Consider that a smaller P-value corresponds to a smaller shaded area under the curve. #### Options: - **Graph (a)** likely represents P = 0.0150 due to its smaller shaded area from the more extreme z-score of \(-2.17\). - **Graph (b)** likely represents P = 0.2776 with a larger shaded region closer to zero at \( z = -0.59 \). **Conclusion:** Understanding the concept behind P-values and normal distributions helps to interpret statistical data effectively. By analyzing the area under the curve for different z-scores, you can determine which graph corresponds to the given P-values without computation.
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