A 90% confidence interval for the proportion of U.S. adults who pay their credit cards in full each month is
A 90% confidence interval for the proportion of U.S. adults who pay their credit cards in full each month is
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Credit Card Debt: Confidence Interval Estimation**
In a survey of 1118 U.S. adults conducted in 2012 by the Financial Industry Regulatory Authority, 810 respondents stated that they always pay their credit cards in full each month. To analyze this data, we will construct a 90% confidence interval for the proportion of U.S. adults who pay their credit cards in full each month. Ensure that the answers are rounded to three decimal places.
A 90% confidence interval for the proportion of U.S. adults who pay their credit cards in full each month is:
\[ \text{_} < p < \text{_} \]
**Instructions**
- Calculate the sample proportion, \( \hat{p} = \frac{810}{1118} \).
- Determine the standard error using the formula \( \text{SE} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \), where \( n \) is the sample size.
- Use the Z-score for a 90% confidence interval (Z = 1.645) to find the margin of error: \( \text{ME} = Z \times \text{SE} \).
- Create the confidence interval: \( \hat{p} - \text{ME} < p < \hat{p} + \text{ME} \).
- Round your final answers to three decimal places.
To ensure comprehension, please follow these steps carefully and verify your calculations with appropriate statistical tools.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87b92f43-2f4d-4033-8a65-475879bd1817%2F762d10e1-59a6-4838-bac0-70bec4c26223%2Fsqtvqd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Credit Card Debt: Confidence Interval Estimation**
In a survey of 1118 U.S. adults conducted in 2012 by the Financial Industry Regulatory Authority, 810 respondents stated that they always pay their credit cards in full each month. To analyze this data, we will construct a 90% confidence interval for the proportion of U.S. adults who pay their credit cards in full each month. Ensure that the answers are rounded to three decimal places.
A 90% confidence interval for the proportion of U.S. adults who pay their credit cards in full each month is:
\[ \text{_} < p < \text{_} \]
**Instructions**
- Calculate the sample proportion, \( \hat{p} = \frac{810}{1118} \).
- Determine the standard error using the formula \( \text{SE} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \), where \( n \) is the sample size.
- Use the Z-score for a 90% confidence interval (Z = 1.645) to find the margin of error: \( \text{ME} = Z \times \text{SE} \).
- Create the confidence interval: \( \hat{p} - \text{ME} < p < \hat{p} + \text{ME} \).
- Round your final answers to three decimal places.
To ensure comprehension, please follow these steps carefully and verify your calculations with appropriate statistical tools.
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