### Understanding Polling Results: Favorite Pie Flavor StudyA magazine conducted a poll among 500 adults to determine their favorite pie. The results provided the following insights:- **14% of respondents chose chocolate pie.**- **The margin of error for this poll is ± 5 percentage points.**The following symbols are used in statistical analysis of the poll results:- \( \hat{p} \): Proportion of the sample choosing chocolate pie- \( \hat{q} \): Proportion of the sample choosing something other than chocolate pie- n: Total number of respondents surveyed- E: Margin of error- p: The true proportion of the entire population's preference for chocolate pie (unknown, estimated by \( \hat{p} \))Given these values, we need to determine what each of these symbols represents, if the confidence level is 90%. Additionally, we need to find the value of \( \alpha \).#### Values- **\( \hat{p} \)**: \(\hat{p} = 0.14\) (14% from the sample)- **\( \hat{q} \)**: \(\hat{q} = 1 - \hat{p} = 0.86\)- **n**: \( n = 500 \) (total respondents)- **E**: \( E = 0.05 \) (5% margin of error)- **p**: (unknown, estimated by \(\hat{p}\))#### Confidence Interval- **Confidence Level**: 90%- **Value of \( \alpha \)**: The significance level (\( \alpha \)) is \( 1 - \text{confidence level} \). Therefore, for a 90% confidence level,\[ \alpha = 1 - 0.90 = 0.10 \]### To Summarize- **The value of \( \hat{p} \) is:** 0.14- **The value of \( \hat{q} \) is:** 0.86- **The value of \( n \) is:** 500- **The value of \( E \) is:** 0.05- **The value of \( p \) is:** estimated by \( \hat{p} \), so approximately 0.14- **The value of \( \alpha ### Understanding Statistical Notation and DefinitionsWhen dealing with statistical notation, it's important to recognize what each symbol represents. Below, we will detail the meanings of common symbols used in statistics. 1. **Symbols and Their Meanings**: - **\(\hat{p}\)**: The value of \(\hat{p}\) refers to the sample proportion. This is an estimate of the true proportion of the population based on the sampled data. - **\(\hat{q}\)**: The value of \(\hat{q}\) is found from evaluating \(1 - \hat{p}\). It represents the proportion of the sample that does not meet the criteria defined by \(\hat{p}\). - **\(n\)**: The value of \(n\) is the sample size. This is the total number of observations or data points in the sample. - **\(E\)**: The value of \(E\) is the margin of error. This quantifies the uncertainty or potential error in the sample estimate and is often used in confidence interval calculations. - **\(p\)**: The value of \(p\) represents the population proportion. This is the true proportion of the population that meets the criteria defined by the research question.2. **Confidence Level and Alpha (\(\alpha\))**: - **\(\alpha\)** represents the level of significance in hypothesis testing. It is typically expressed as a decimal (e.g., 0.05) and corresponds to the probability of making a Type I error, which is rejecting a true null hypothesis. 3. **User Input**: - Users are typically asked to input the value of \(\alpha\) in hypothesis testing scenarios. For example, if you want a 95% confidence level, then \(\alpha\) would be 0.05.### Interactive ExampleConsider the following multiple-choice question to reinforce your understanding:#### Question: What does the symbol \(\hat{p}\) represent? - [ ] the sample size. - [ ] the population proportion. - [ ] the margin of error. - [X] the sample proportion. - [ ] found from evaluating \(1 - \hat{p}\).By providing these explanations and interactive questions, students can practice and enhance their understanding of statistical symbols and concepts.

Given , Among the 500 respondent 14 chose chocolate pie , and margin of error was given as 5

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 14% chose chocolate pie, and the margin of error was given as ±5 percentage points. What values do p, q, n, E, and p represent? If the confidence level is 90%, what is the value of a? The value of p is The value of q is The value of n is The value of E is The value of p is If the confidence level is 90%, what is the value of a? |(Type an integer or a decimal. Do not round.) α

A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 14% chose chocolate pie, and the margin of error was given as ±5 percentage points. What values do p, q, n, E, and p represent? If the confidence level is 90%, what is the value of a? The value of p is The value of q is The value of n is The value of E is The value of p is If the confidence level is 90%, what is the value of a? |(Type an integer or a decimal. Do not round.) α

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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