If n = 140 and p (p-hat) = 0.7, construct a 90% confidence interval. %3D %3D Give your answers to three decimals
If n = 140 and p (p-hat) = 0.7, construct a 90% confidence interval. %3D %3D Give your answers to three decimals
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Question 10
If \( n = 140 \) and \(\hat{p} \) (p-hat) = 0.7, construct a 90% confidence interval.
Give your answers to three decimals.
\[ \_\_\_ < p < \_\_\_ \]
**Question Help:** [Video]
**Submit Question**
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This prompt is asking you to calculate a 90% confidence interval for a proportion based on the given sample size (\( n = 140 \)) and the sample proportion (\(\hat{p} = 0.7\)). You need to provide the lower and upper bounds of the confidence interval, rounded to three decimal places, and input them in the provided text boxes.
### Explanation:
- \( \hat{p} \) represents the sample proportion.
- The confidence interval gives a range that likely contains the true population proportion.
- A 90% confidence interval reflects that if the same population was sampled repeatedly, 90% of the intervals would contain the true proportion.
To calculate the confidence interval:
1. Find the standard error (SE) using the formula \( SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \).
2. Determine the Z-score for a 90% confidence level (typically 1.645).
3. Calculate the margin of error (ME) using \( ME = Z \times SE \).
4. The confidence interval is \(\hat{p} - ME < p < \hat{p} + ME\).
Make sure to check the video linked for additional guidance if needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F956ba92b-4eda-474e-a055-a4f5efb50eed%2F292885e6-ccde-4a3e-921a-d47603268190%2Fqce0uj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 10
If \( n = 140 \) and \(\hat{p} \) (p-hat) = 0.7, construct a 90% confidence interval.
Give your answers to three decimals.
\[ \_\_\_ < p < \_\_\_ \]
**Question Help:** [Video]
**Submit Question**
---
This prompt is asking you to calculate a 90% confidence interval for a proportion based on the given sample size (\( n = 140 \)) and the sample proportion (\(\hat{p} = 0.7\)). You need to provide the lower and upper bounds of the confidence interval, rounded to three decimal places, and input them in the provided text boxes.
### Explanation:
- \( \hat{p} \) represents the sample proportion.
- The confidence interval gives a range that likely contains the true population proportion.
- A 90% confidence interval reflects that if the same population was sampled repeatedly, 90% of the intervals would contain the true proportion.
To calculate the confidence interval:
1. Find the standard error (SE) using the formula \( SE = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \).
2. Determine the Z-score for a 90% confidence level (typically 1.645).
3. Calculate the margin of error (ME) using \( ME = Z \times SE \).
4. The confidence interval is \(\hat{p} - ME < p < \hat{p} + ME\).
Make sure to check the video linked for additional guidance if needed.
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