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Let p be the population proportion for the following condition. Find the point estimates for p and q. Of 928 children surveyed, 122 plan to join the armed forces in the future. ..... The point estimate for p, p, is . (Round to three decimal places as needed.) Vi Vi (1,1) TC

Let p be the population proportion for the following condition. Find the point estimates for p and q. Of 928 children surveyed, 122 plan to join the armed forces in the future. ..... The point estimate for p, p, is . (Round to three decimal places as needed.) Vi Vi (1,1) TC

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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In this educational exercise, we are tasked with finding the point estimate for the population proportion (denoted as \( p \)) and its complementary probability (denoted as \( q \)) based on survey data. **Problem Statement:** Let \( p \) be the population proportion for the following condition. Find the point estimates for \( p \) and \( q \). - **Data Given:** - Out of 928 children surveyed, 122 plan to join the armed forces in the future. **Solution:** To find the point estimate for \( p \), which is the proportion of children planning to join the armed forces, use the formula: \[ \hat{p} = \frac{x}{n} \] where: - \( x = 122 \) (number of children planning to join) - \( n = 928 \) (total number of children surveyed) Substitute the given values: \[ \hat{p} = \frac{122}{928} \] Calculate and round to three decimal places as needed to obtain the final point estimate. Once \( \hat{p} \) is determined, the point estimate for \( q \), which is the proportion of children not planning to join the armed forces, can be found using: \[ \hat{q} = 1 - \hat{p} \] **Additional Features:** - **User Interface Options:** - Help Me Solve This - View an Example - Get More Help - Clear All - Check Answer These options provide tools for step-by-step guidance, examples for better understanding, and a feature to check the correctness of the calculated answer.
Transcribed Image Text:In this educational exercise, we are tasked with finding the point estimate for the population proportion (denoted as \( p \)) and its complementary probability (denoted as \( q \)) based on survey data. **Problem Statement:** Let \( p \) be the population proportion for the following condition. Find the point estimates for \( p \) and \( q \). - **Data Given:** - Out of 928 children surveyed, 122 plan to join the armed forces in the future. **Solution:** To find the point estimate for \( p \), which is the proportion of children planning to join the armed forces, use the formula: \[ \hat{p} = \frac{x}{n} \] where: - \( x = 122 \) (number of children planning to join) - \( n = 928 \) (total number of children surveyed) Substitute the given values: \[ \hat{p} = \frac{122}{928} \] Calculate and round to three decimal places as needed to obtain the final point estimate. Once \( \hat{p} \) is determined, the point estimate for \( q \), which is the proportion of children not planning to join the armed forces, can be found using: \[ \hat{q} = 1 - \hat{p} \] **Additional Features:** - **User Interface Options:** - Help Me Solve This - View an Example - Get More Help - Clear All - Check Answer These options provide tools for step-by-step guidance, examples for better understanding, and a feature to check the correctness of the calculated answer.
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