Choose one statement for each question **Title: Understanding Statistical Terms from a Poll on Favorite Pie**A magazine conducted a poll involving 1000 adults to identify their favorite pie. Out of the 1000 respondents, 12% chose chocolate pie. Additionally, the margin of error was provided as ± 3 percentage points. This example serves to explain various statistical terms used to interpret the poll results. Let's explore the values of $\hat{p}$, $\hat{q}$, $n$, $E$, and $p$, and understand their significance. Furthermore, we will determine the value of $\alpha$ for a 90% confidence level.### Definitions and Values:1. **$\hat{p}$ (Sample Proportion):** - $\hat{p}$ is the proportion of the sample that chose chocolate pie. - Given in the poll: $\hat{p} = 0.12$ or 12%.2. **$\hat{q}$ (Complement of Sample Proportion):** - $\hat{q}$ represents the proportion of the sample that did not choose chocolate pie. - Calculated as $1 - \hat{p}$: \[\hat{q} = 1 - 0.12 = 0.88\]3. **$n$ (Sample Size):** - The number of respondents surveyed. - Given in the poll: $n = 1000$.4. **$E$ (Margin of Error):** - The margin of error, representing the range within which the true population proportion is expected to lie. - Given in the poll: $E = 3\%$ or $0.03$. 5. **$p$ (Population Proportion):** - The true proportion of the population that prefers chocolate pie, which can be estimated using $\hat{p}$.### Confidence Level and Alpha ($\alpha$):- **Confidence Level:** The degree of certainty that the population proportion lies within the margin of error. - For a 90% confidence level, $\alpha = 1 - \text{confidence level}$: \[\alpha = 1 - 0.90 = 0.10\]Based on this information, the values are:- \(\hat{p} = 0.12\

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Description: Choose one statement for each question **Title: Understanding Statistical Terms from a Poll on Favorite Pie**A magazine conducted a poll involving 1000 adults to identify their favorite pie. Out of the 1000 respondents, 12% chose chocolate pie. Addit

Confidence level : 90 % = 0.9 value of alpha = 1 - 0.9 = 0.1

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A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 respondents, 12% chose chocolate pie, and the margin of error was given as ± 3 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 population proportion. The value of q is the margin of error. The value ofn is The value of E is the population proportion. The value of p is the sample size. found from evaluating 1-p. the sample proportion.

A magazine provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 respondents, 12% chose chocolate pie, and the margin of error was given as ± 3 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 population proportion. The value of q is the margin of error. The value ofn is The value of E is the population proportion. The value of p is the sample size. found from evaluating 1-p. the sample proportion.

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Choose one statement for each question

**Title: Understanding Statistical Terms from a Poll on Favorite Pie**

A magazine conducted a poll involving 1000 adults to identify their favorite pie. Out of the 1000 respondents, 12% chose chocolate pie. Additionally, the margin of error was provided as ± 3 percentage points. This example serves to explain various statistical terms used to interpret the poll results. Let's explore the values of $\hat{p}$, $\hat{q}$, $n$, $E$, and $p$, and understand their significance. Furthermore, we will determine the value of $\alpha$ for a 90% confidence level.

### Definitions and Values:

1. **$\hat{p}$ (Sample Proportion):**
- $\hat{p}$ is the proportion of the sample that chose chocolate pie.
- Given in the poll: $\hat{p} = 0.12$ or 12%.

2. **$\hat{q}$ (Complement of Sample Proportion):**
- $\hat{q}$ represents the proportion of the sample that did not choose chocolate pie.
- Calculated as $1 - \hat{p}$:
\[\hat{q} = 1 - 0.12 = 0.88\]

3. **$n$ (Sample Size):**
- The number of respondents surveyed.
- Given in the poll: $n = 1000$.

4. **$E$ (Margin of Error):**
- The margin of error, representing the range within which the true population proportion is expected to lie.
- Given in the poll: $E = 3\%$ or $0.03$.

5. **$p$ (Population Proportion):**
- The true proportion of the population that prefers chocolate pie, which can be estimated using $\hat{p}$.

### Confidence Level and Alpha ($\alpha$):

- **Confidence Level:** The degree of certainty that the population proportion lies within the margin of error.
- For a 90% confidence level, $\alpha = 1 - \text{confidence level}$:
\[\alpha = 1 - 0.90 = 0.10\]

Based on this information, the values are:
- \(\hat{p} = 0.12\

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