https://file.aiquickdraw.com/mathbot/file/173007540162104nfrjff.jpg

Let's walk through the solution step-by-step using the data from the image:

### 1. **What is the population parameter?**  
- **Answer:** The **population parameter** refers to the true proportion of all employees in the company who do not feel financially prepared for retirement.  
(Select: **Population proportion of employees who do not feel prepared for retirement**)

---

### 2. **What is the point estimate for the population proportion? \( \hat{p} \)**  
The formula for the sample proportion \( \hat{p} \) is:

\[
\hat{p} = \frac{\text{Number of employees who feel unprepared}}{\text{Sample size (n)}}
\]

Using the given dataLet's walk through the solution step-by-step using the data from the image:

### 1. **What is the population parameter?**  
- **Answer:** The **population parameter** refers to the true proportion of all employees in the company who do not feel financially prepared for retirement.  
(Select: **Population proportion of employees who do not feel prepared for retirement**)

---

### 2. **What is the point estimate for the population proportion? \( \hat{p} \)**  
The formula for the sample proportion \( \hat{p} \) is:

\[
\hat{p} = \frac{\text{Number of employees who feel unprepared}}{\text{Sample size (n)}}
\]

Using the given 
\[
\hat{p} = \frac{72}{100} = 0.72
\]

So, the **point estimate** for the population proportion \( \hat{p} \) is 0.72.

---

### 3. **Confidence Interval Interpretation**  
The confidence interval for a proportion is calculated as:

\[
\hat{p} \pm \text{Margin of Error}
\]

Given:
- \( \hat{p} = 0.72 \)
- Margin of Error = 0.104

Thus, the confidence interval is:

\[
0.72 - 0.104 = 0.616
\]
\[
0.72 + 0.104 = 0.824
\]

The data suggests a **99% confidence** that the proportion of employees who do not feel prepared is between **0.616** and **0.824**.

(Select: **99%** confidence, and fill in the interval: [0.616, 0.824])

---

### 4. **Largest Likely Proportion of Employees Attending the Seminar**  
Since the seminar targets employees who do **not** feel prepared, the **largest likely proportion** that will attend corresponds to the **upper bound** of the confidence interval.

- **Answer:** The largest likely proportion is **0.824**.

---

### Summary of Answers:
- **Population Parameter:** Proportion of all employees who do not feel prepared for retirement.
- **Point Estimate:** \( \hat{p} = 0.72 \)
- **Confidence Level:** 99%
- **Confidence Interval:** [0.616, 0.824]
- **Largest Likely Proportion Attending the Seminar:** 0.824

Do you want more details on any step? 

---

Here are 5 additional related questions for deeper exploration:
1. What would happen to the margin of error if the sample size was increased?
2. How would the confidence interval change if a 95% confidence level was used?
3. What assumptions are made when constructing this confidence interval?
4. How does increasing the sample size affect the reliability of the point estimate?
5. What are Type I and Type II errors, and how do they relate to this type of survey?

**Tip:** Confidence intervals are most informative when the margin of error is small, indicating greater precision in the estimate.

A company wants to determine the largest likely proportion of employees who do not feel financially prepared for retirement based on a sample. The problem involves calculating a point estimate, constructing a confidence interval, and finding the largest likely proportion for a seminar.

Learn how to calculate a point estimate and a confidence interval for a sample of employees who feel unprepared for retirement. This problem walks through determining the population parameter, constructing a 99% confidence interval, and finding the largest likely proportion for seminar attendance.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation