A phase three clinical trial testing a new sleeping pill has 1347 participants. If all these individuals are from the group of individuals who were given the medication and 620 individuals who received the medication experienced drug-induced mental impairment, construct a 95% confidence interval for the true proportion of individuals on the medication who experienced drug-induced mental impairment.
A phase three clinical trial testing a new sleeping pill has 1347 participants. If all these individuals are from the group of individuals who were given the medication and 620 individuals who received the medication experienced drug-induced mental impairment, construct a 95% confidence interval for the true proportion of individuals on the medication who experienced drug-induced mental impairment.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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The answer I keep getting is (.434, .487)
N=1347
x=620
CI=.95
Z=1.96
Thanks
Roy
![### Confidence Interval in Clinical Trials
#### Question 6
A phase three clinical trial testing a new sleeping pill has 1347 participants. If all these individuals are from the group of individuals who were given the medication and 620 individuals who received the medication experienced drug-induced mental impairment, construct a 95% confidence interval for the true proportion of individuals on the medication who experienced drug-induced mental impairment.
Options:
- (0.452, 0.468)
- (0.451, 0.469)
- (0.448, 0.472)
- (0.450, 0.470)
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##### Explanation:
A confidence interval is a range of values, derived from a data sample, that is likely to contain the value of an unknown population parameter. In this case, we are looking to estimate the proportion of participants who experienced drug-induced mental impairment.
To construct this interval, we have a sample proportion (p-hat) and standard error (SE). The formula for the confidence interval at a 95% confidence level is:
\[ \text{CI} = \hat{p} \pm Z \cdot \text{SE} \]
Where:
- \( \hat{p} \) is the sample proportion
- \( Z \) is the Z-value from the standard normal distribution corresponding to the desired confidence level (1.96 for 95%)
- \( \text{SE} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \)
Given:
- Sample size (n) = 1347
- Participants with impairment = 620
- Sample proportion (\( \hat{p} \)) = \( \frac{620}{1347} \approx 0.460 \)
Calculate the standard error and use the formula to find the interval. Use the given options to choose the correct confidence interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd97ecd7b-3655-4fc2-852b-d38cea023445%2Fd3e2111e-1585-4785-a05e-3efac08dea26%2Fsf1gf8f.png&w=3840&q=75)
Transcribed Image Text:### Confidence Interval in Clinical Trials
#### Question 6
A phase three clinical trial testing a new sleeping pill has 1347 participants. If all these individuals are from the group of individuals who were given the medication and 620 individuals who received the medication experienced drug-induced mental impairment, construct a 95% confidence interval for the true proportion of individuals on the medication who experienced drug-induced mental impairment.
Options:
- (0.452, 0.468)
- (0.451, 0.469)
- (0.448, 0.472)
- (0.450, 0.470)
**Navigation Buttons:**
- [PREVIOUS]
- [NEXT]
##### Explanation:
A confidence interval is a range of values, derived from a data sample, that is likely to contain the value of an unknown population parameter. In this case, we are looking to estimate the proportion of participants who experienced drug-induced mental impairment.
To construct this interval, we have a sample proportion (p-hat) and standard error (SE). The formula for the confidence interval at a 95% confidence level is:
\[ \text{CI} = \hat{p} \pm Z \cdot \text{SE} \]
Where:
- \( \hat{p} \) is the sample proportion
- \( Z \) is the Z-value from the standard normal distribution corresponding to the desired confidence level (1.96 for 95%)
- \( \text{SE} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \)
Given:
- Sample size (n) = 1347
- Participants with impairment = 620
- Sample proportion (\( \hat{p} \)) = \( \frac{620}{1347} \approx 0.460 \)
Calculate the standard error and use the formula to find the interval. Use the given options to choose the correct confidence interval.
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