Let's go through each part of the question based on the information provided.

1. Population Parameter: The population parameter here is the true proportion of satisfied customers in the population, which the airline aims to estimate.

2. Point Estimate for the Population Proportion $\hat{p}$:

   • The point estimate of the population proportion $\hat{p}$ is calculated by dividing the number of satisfied customers in the sample by the total sample size. $\hat{p} = \frac{186}{500} = 0.372$

3. Confidence Level: Given as 90%.

4. Confidence Interval for the Population Proportion:

   • The confidence interval for a proportion is given by: $\hat{p} \pm \text{Margin of Error}$ Here, the margin of error is provided as 0.028.

   So, the confidence interval is: $0.372 \pm 0.028 = [0.344, 0.400]$

5. Lowest Likely Proportion:

   • The lowest likely proportion of satisfied customers, based on the confidence interval, is the lower bound: $0.344$

Summary of Answers:

• Population Parameter: True proportion of satisfied customers.
• Point Estimate $\hat{p}$: $0.372$
• Confidence Level: 90%
• Confidence Interval: [0.344, 0.400]
• Lowest Likely Proportion: $0.344$

Would you like more detailed explanations on any part of the solution?

Here are 5 related questions to further your understanding:

1. How is the critical value chosen based on the confidence level?
2. Why is the point estimate calculated as $\frac{186}{500}$ in this case?
3. How does the sample size affect the margin of error?
4. What would happen to the confidence interval if the sample size were larger?
5. How would the confidence interval change with a 95% confidence level instead of 90%?

Tip: Remember, the confidence interval provides a range of plausible values for the population parameter based on the sample data and the specified confidence level.