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A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 12% 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 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 If the confidence level is 99%, what is the value of a? (Type an integer or a decimal. Do not round.) ▼ a=

A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 12% 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 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 If the confidence level is 99%, what is the value of a? (Type an integer or a decimal. Do not round.) ▼ a=

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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### Poll Results and Statistical Analysis **Survey Overview:** A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 12% chose chocolate pie. The margin of error (E) was given as ±4 percentage points. **Values to Determine:** - $\hat{p}$: Sample proportion of respondents who chose chocolate pie. - $\hat{q}$: Sample proportion of respondents who did not choose chocolate pie. - $n$: The sample size. - $E$: Margin of error. - $p$: The population proportion (not known but estimated by $\hat{p}$). **Confidence Level:** If the confidence level is 99%, we need to determine the value of $\alpha$. ### Detailed Explanation of Variables: - **The value of $\hat{p}$:** The sample proportion of those who chose chocolate pie is 12%, which is 0.12. - **The value of $\hat{q}$:** The sample proportion of those who did not choose chocolate pie is the complement of $\hat{p}$, which is \(1 - \hat{p}\). Therefore, $\hat{q}$ is \(1 - 0.12 = 0.88\). - **The value of $n$:** The sample size, $n$, is the total number of respondents, which is 2000. - **The value of $E$:** The margin of error given for the poll results is ±4 percentage points, which is 0.04. - **The value of $p$:** The population proportion is usually unknown but is estimated by the sample proportion, which means $\hat{p}$ is used as an estimate. Thus, $p$ is approximately 0.12. **Determining $\alpha$:** The confidence level is 99%, which means that $\alpha = 1 - 0.99 = 0.01$. Hence, $\alpha$ is 0.01. ### Quick Summary: - **$\hat{p}$:** 0.12 - **$\hat{q}$:** 0.88 - **$n$:** 2000 - **$E$:** 0.04 - **$p$:** Approximately 0.12 - **$\alpha$:** 0.01 (for a
Transcribed Image Text:### Poll Results and Statistical Analysis **Survey Overview:** A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 12% chose chocolate pie. The margin of error (E) was given as ±4 percentage points. **Values to Determine:** - $\hat{p}$: Sample proportion of respondents who chose chocolate pie. - $\hat{q}$: Sample proportion of respondents who did not choose chocolate pie. - $n$: The sample size. - $E$: Margin of error. - $p$: The population proportion (not known but estimated by $\hat{p}$). **Confidence Level:** If the confidence level is 99%, we need to determine the value of $\alpha$. ### Detailed Explanation of Variables: - **The value of $\hat{p}$:** The sample proportion of those who chose chocolate pie is 12%, which is 0.12. - **The value of $\hat{q}$:** The sample proportion of those who did not choose chocolate pie is the complement of $\hat{p}$, which is \(1 - \hat{p}\). Therefore, $\hat{q}$ is \(1 - 0.12 = 0.88\). - **The value of $n$:** The sample size, $n$, is the total number of respondents, which is 2000. - **The value of $E$:** The margin of error given for the poll results is ±4 percentage points, which is 0.04. - **The value of $p$:** The population proportion is usually unknown but is estimated by the sample proportion, which means $\hat{p}$ is used as an estimate. Thus, $p$ is approximately 0.12. **Determining $\alpha$:** The confidence level is 99%, which means that $\alpha = 1 - 0.99 = 0.01$. Hence, $\alpha$ is 0.01. ### Quick Summary: - **$\hat{p}$:** 0.12 - **$\hat{q}$:** 0.88 - **$n$:** 2000 - **$E$:** 0.04 - **$p$:** Approximately 0.12 - **$\alpha$:** 0.01 (for a
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