### 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

See similar textbooks

Similar questions

Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=931 and x=548 who said "yes." Use a 99% confidence level. LOADING... Click the icon to view a table of z scores. b) Identify the value of the margin of error E.
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=935 and x=561 who said "yes." Use a 95% confidence level.
B. Identify the value of the margin of error E C. Construct the confidence interval There are 3 part to this question. Other two questions are above.
Construct a 95% confidence interval for p1 - p2 for a survey that finds 30% of 240 males and 41% of 200 females are opposed to the death penalty. Group of answer choices a.(-0.200, -0.021) b.(-1.532, 1.342) c.(-1.324, 1.512) d.(-0.561, 0.651)
A survey asked, "How important is it to you to buy products that are made in America?" of the 600 Americans surveyed, 450 responded, "It is important." For each of the following levels of confidence, find the sample proportion and the margin of error (MOE) associated with the poll. (Give the answers to one decimal place, if needed.) A 95% level of confidenceSample proportion is %MOE = %
A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 respondents, 11% 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 99%, 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
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie Among the 500 respondents, 13% chose chocolate pie, and the margin of error was given as +4 percentage points. What values do p, q, n, E, and p represent? If the confidence level is 95%, 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 95%, what is the value of a? (Type an integer or a decimal. Do not round.)
In a recent poll, 500 people were asked if they liked dogs, and 72% said they did. Find the margin of error of this poll, at the 95% confidence level. Give your answer to three decimals
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n= 1004 and x = 575 who said "yes." Use a 90% confidence level. E Click the icon to view a table of z scores. .... a) Find the best point estimate of the population proportion p. (Round to three decimal places as needed.)
In a recent poll, 570 people were asked if they liked dogs, and 14% said they did. Find the margin of error of this poll, at the 95% confidence level.Give your answer to three decimals
Save Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n= 974 and x= 526 who said "yes." Use a 90% confidence level. Click the icon to view a table of z scores. a) Find the best point estimate of the population proportion p. (Round to three decimal places as needed.)
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 1005 and x = 580 who said "yes." Use a 95% confidence level. Click the icon to view a table of z scores. a) Find the best point estimate of the population proportion p. (Round to three decimal places as needed.) ew an example Get more help. MacBook Air ... Clear all Chec.