Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 195, x = 162; 95% confidence A) 0.789 < p < 0.873 %3D B) 0.778 < p < 0.883 C) 0.788
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p. n = 195, x = 162; 95% confidence A) 0.789 < p < 0.873 %3D B) 0.778 < p < 0.883 C) 0.788
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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![**Question 71: Confidence Interval Construction**
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion \( p \).
- Sample size (\( n \)): 195
- Number of successes (\( x \)): 162
- Confidence level: 95%
Possible answer choices:
A) \( 0.789 < p < 0.873 \)
B) \( 0.778 < p < 0.883 \)
C) \( 0.788 < p < 0.873 \)
D) \( 0.777 < p < 0.884 \)
**Explanation:**
To construct a confidence interval for a population proportion, you can use the formula for a confidence interval for a proportion, which is given by:
\[ \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]
Where:
- \( \hat{p} \) is the sample proportion, calculated by \( x/n \).
- \( Z \) is the Z-score corresponding to the desired confidence level.
- \( n \) is the sample size.
Calculate \( \hat{p} \), determine the Z-score for 95% confidence, and use the formula to find the correct interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4d5b940-4227-4804-a5a1-28e36f78c013%2F6ccf389e-81b6-4290-b4f1-e86971e8a14e%2Fz6jgthb_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 71: Confidence Interval Construction**
Use the given degree of confidence and sample data to construct a confidence interval for the population proportion \( p \).
- Sample size (\( n \)): 195
- Number of successes (\( x \)): 162
- Confidence level: 95%
Possible answer choices:
A) \( 0.789 < p < 0.873 \)
B) \( 0.778 < p < 0.883 \)
C) \( 0.788 < p < 0.873 \)
D) \( 0.777 < p < 0.884 \)
**Explanation:**
To construct a confidence interval for a population proportion, you can use the formula for a confidence interval for a proportion, which is given by:
\[ \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \]
Where:
- \( \hat{p} \) is the sample proportion, calculated by \( x/n \).
- \( Z \) is the Z-score corresponding to the desired confidence level.
- \( n \) is the sample size.
Calculate \( \hat{p} \), determine the Z-score for 95% confidence, and use the formula to find the correct interval.
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