https://file.aiquickdraw.com/mathbot/file/17300755423234jp2yjk5.jpg

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.

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 - 186, Sample size (n) - 500, Confidence Level - 90%, Critical Value - 1.282, Margin of Error - 0.028. What is the population parameter? What is the point estimate for the population proportion? The data suggests a confidence exists that the proportion of customers in the sample that are satisfied is between [ , ]. Thus, the lowest likely proportion of customers that are satisfied is .

Learn how to determine the lowest likely proportion of satisfied customers in a sample of 500, with 186 satisfied responses, using a 90% confidence interval. Understand the calculation of population proportion, point estimates, and confidence intervals for statistics students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation