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To solve this problem, let's go through each part of the question step-by-step.

### Given Information
- Number of satisfied customers: \( 426 \)
- Sample size (\( n \)): \( 1000 \)
- Confidence level: \( 95\% \)
- Critical value (Z-score for 95% confidence level): \( 1.645 \)
- Margin of error: \( 0.026 \)

### Solution

1. **Population Parameter**:
   The population parameter we're estimating is the **population proportion** of satisfied customers. 

2. **Point Estimate for Population Proportion (\( \hat{p} \))**:
   The point estimate for the population proportion, \( \hat{p} \), is calculated by dividing the number of satisfied customers by the total sample size:
   \[
   \hat{p} = \frac{426}{1000} = 0.426
   \]

3. **Confidence Interval Calculation**:
   Since the margin of error is given as \( 0.026 \), we can construct the confidence interval for the proportion of satisfied customers by adding and subtracting this margin of error from \( \hat{p} \).

   - **Lower bound** of the confidence interval:
     \[
     \text{Lower bound} = \hat{p} - \text{Margin of Error} = 0.426 - 0.026 = 0.400
     \]
   
   - **Upper bound** of the confidence interval:
     \[
     \text{Upper bound} = \hat{p} + \text{Margin of Error} = 0.426 + 0.026 = 0.452
     \]

   So, the confidence interval is between **0.400** and **0.452**.

4. **Lowest Likely Proportion of Satisfied Customers**:
   The lowest likely proportion of satisfied customers, based on the confidence interval, is the **lower bound**, which is **0.400**.

### Answers Summary
- **Population Parameter**: Proportion of satisfied customers.
- **Point Estimate** (\( \hat{p} \)): \( 0.426 \)
- **Confidence Level**: \( 95\% \)
- **Confidence Interval**: Between \( 0.400 \) and \( 0.452 \)
- **Lowest Likely Proportion of Satisfied Customers**: \( 0.400 \)

Would you like more details on any step? 

Here are some related questions:
1. How do we interpret a confidence interval in this context?
2. What is the relationship between sample size and margin of error?
3. How would the confidence interval change with a 99% confidence level?
4. Why is the point estimate considered the best estimate of the population proportion?
5. How is the critical value chosen for different confidence levels?

**Tip**: Confidence intervals provide a range of plausible values for the population parameter and give insights into the accuracy of our sample estimate.

An airline wants to know the lowest likely proportion of satisfied customers. The airline surveys a random sample of customers. The results of the sample are shown below:

- Satisfied: 426
- Sample size (n): 1000
- Confidence Level: 95%
- Critical Value: 1.645
- Margin of Error: 0.026

What is the population parameter?
What is the point estimate for the population proportion?
The data suggests a confidence interval exists that the proportion of customers in the sample that are satisfied is between a lower bound and an upper bound.
Thus, the lowest likely proportion of customers that are satisfied is ______.

Learn how to determine the lowest likely proportion of satisfied customers based on a random sample. Using a 95% confidence level, critical value of 1.645, and margin of error of 0.026, calculate the confidence interval and point estimate for customer satisfaction.

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