If n = 340 and p (p-hat) = 0.05, construct a 90% confidence Interval. Give your answers to three decimals
If n = 340 and p (p-hat) = 0.05, construct a 90% confidence Interval. 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
If n= 340 and p^ ( p-hat)= 0.05, construct a 90% confidence interval.
Give your answers to three decimals
![### Constructing a 90% Confidence Interval
To construct a 90% confidence interval for a population proportion, follow these instructions:
Given:
- Sample size (\( n \)) = 340
- Sample proportion (\( \hat{p} \)) = 0.05
**Task**: Calculate the 90% confidence interval for the population proportion. Provide your answers to three decimal places.
#### Steps:
1. **Determine the Standard Error (SE):**
The standard error for the sample proportion is calculated using the formula:
\[
SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}
\]
2. **Find the Z-score for a 90% Confidence Level:**
The Z-score associated with a 90% confidence level is approximately 1.645.
3. **Calculate the Confidence Interval:**
The confidence interval is given by:
\[
\hat{p} \pm Z \times SE
\]
4. **Substitute the Values:**
Calculate and fill in the results in the boxes below:
\[
< p <
\]
Enter your calculated confidence interval below and submit your response.
**Submit Question Button**: Use this button once your answers are entered.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce79cdf7-b1ae-4527-8afa-a8738b654041%2F73d67f1d-f8fb-4364-b1c8-208d52eb7ec0%2F6ndjp7m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Constructing a 90% Confidence Interval
To construct a 90% confidence interval for a population proportion, follow these instructions:
Given:
- Sample size (\( n \)) = 340
- Sample proportion (\( \hat{p} \)) = 0.05
**Task**: Calculate the 90% confidence interval for the population proportion. Provide your answers to three decimal places.
#### Steps:
1. **Determine the Standard Error (SE):**
The standard error for the sample proportion is calculated using the formula:
\[
SE = \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}
\]
2. **Find the Z-score for a 90% Confidence Level:**
The Z-score associated with a 90% confidence level is approximately 1.645.
3. **Calculate the Confidence Interval:**
The confidence interval is given by:
\[
\hat{p} \pm Z \times SE
\]
4. **Substitute the Values:**
Calculate and fill in the results in the boxes below:
\[
< p <
\]
Enter your calculated confidence interval below and submit your response.
**Submit Question Button**: Use this button once your answers are entered.
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