**Problem Statement: Analyzing Proportional Support in Phoenix**The proportion of residents in Phoenix favoring the building of toll roads to complete the freeway system is believed to be \( \rho = 0.3 \). If a random sample of 10 residents shows 1 or fewer favor this proposal, we will conclude that \( \rho < 0.3 \).1. **Find the probability of Type I error if the true proportion is \( \rho = 0.3 \).** 2. **Find the probability of committing a Type II error with this procedure if \( \rho = 0.3 \).**3. **What is the power of this procedure if the true proportion is \( \rho = 0.2 \)?****Explanation of Concepts:**- **Type I Error:** Occurs when the null hypothesis is rejected when it is actually true. Calculating this probability helps understand the risk of making a false positive conclusion.- **Type II Error:** Involves failing to reject the null hypothesis when it is false. This indicates a false negative result, suggesting the procedure’s inability to detect an actual effect.- **Power of a Test:** Represents the probability that the test correctly rejects a false null hypothesis. Power is 1 minus the probability of a Type II error, showing the effectiveness of the test in identifying true effects.

The proportion of residents in Phoenix favoring the building of toll roads to complete the freeway system is believed to be p= 0.3. If a random sample of 10 residents shows 1 or fewer favor this proposal, we will conclude that p< 0.3. 1. Find the probability of type I error if the true proportion is p= 0.3. 2. Find the probability of committing a type II error with this procedure is p= 0.3. 3. What is the power this procedure if the true proportion is p= 0.2? %3D

The proportion of residents in Phoenix favoring the building of toll roads to complete the freeway system is believed to be p= 0.3. If a random sample of 10 residents shows 1 or fewer favor this proposal, we will conclude that p< 0.3. 1. Find the probability of type I error if the true proportion is p= 0.3. 2. Find the probability of committing a type II error with this procedure is p= 0.3. 3. What is the power this procedure if the true proportion is p= 0.2? %3D

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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