Content / Stat Lit and Crit Reasoning DENCE INTERVALS AND HYPOTHESIS TESTING ence interval for the population mean: Use of the standar... t: Colorado is interested in finding the mean chloride level for a healthy resident in the state. A random sample of 150 healt mEq level of 103 L If it is known that the chloride levels in healthy individuals residing in Colorado have a standard deviat ce interval for the true mean chloride level of all healthy Colorado residents. Then give its lower limit and upper limit. ermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult X ALEKS-Mand S
Content / Stat Lit and Crit Reasoning DENCE INTERVALS AND HYPOTHESIS TESTING ence interval for the population mean: Use of the standar... t: Colorado is interested in finding the mean chloride level for a healthy resident in the state. A random sample of 150 healt mEq level of 103 L If it is known that the chloride levels in healthy individuals residing in Colorado have a standard deviat ce interval for the true mean chloride level of all healthy Colorado residents. Then give its lower limit and upper limit. ermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult X ALEKS-Mand S
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![### Confidence Intervals and Hypothesis Testing
#### Confidence Interval for the Population Mean: Use of the Standard Error
A laboratory in Colorado is interested in finding the mean chloride level for a healthy resident in the state. A random sample of 150 healthy residents has a mean chloride level of 103 mEq/L. If it is known that the chloride levels in healthy individuals residing in Colorado have a standard deviation of 44 mEq/L, find a 90% confidence interval for the true mean chloride level of all healthy Colorado residents. Then give its lower limit and upper limit.
##### Steps to Calculate the Confidence Interval:
1. Identify the sample mean (\( \bar{x} \)): 103 mEq/L
2. Identify the sample size (\( n \)): 150
3. Identify the standard deviation (\( \sigma \)): 44 mEq/L
4. Determine the confidence level (90%), which corresponds to a critical z-value (typically found using a z-table or statistical software).
The formula for the confidence interval is given by:
\[ \bar{x} \pm z \left( \frac{\sigma}{\sqrt{n}} \right) \]
Where:
- \( \bar{x} \) is the sample mean
- \( z \) is the z-value corresponding to the desired confidence level
- \( \sigma \) is the population standard deviation
- \( n \) is the sample size
5. Calculate the standard error (SE):
\[ SE = \frac{\sigma}{\sqrt{n}} \]
6. Use the critical z-value for a 90% confidence interval (which is approximately 1.645 for a two-tailed test).
7. Calculate the margin of error (ME):
\[ ME = z \times SE \]
8. Determine the lower and upper limits of the confidence interval:
\[ \text{Lower limit} = \bar{x} - ME \]
\[ \text{Upper limit} = \bar{x} + ME \]
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
##### Input Fields:
- **Lower limit:**
- **Upper limit:**
---
This educational problem involves calculating the confidence interval for the true mean chloride level in Colorado residents by using the known sample statistics. This exercise helps in understanding the application of confidence intervals in statistics, specifically for estimating population parameters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff3529348-32c4-44c7-a2a9-c73ae444d8be%2F9262d328-51b0-4a1e-93a4-a18f50d3b0f9%2Fm3o4bfxf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Confidence Intervals and Hypothesis Testing
#### Confidence Interval for the Population Mean: Use of the Standard Error
A laboratory in Colorado is interested in finding the mean chloride level for a healthy resident in the state. A random sample of 150 healthy residents has a mean chloride level of 103 mEq/L. If it is known that the chloride levels in healthy individuals residing in Colorado have a standard deviation of 44 mEq/L, find a 90% confidence interval for the true mean chloride level of all healthy Colorado residents. Then give its lower limit and upper limit.
##### Steps to Calculate the Confidence Interval:
1. Identify the sample mean (\( \bar{x} \)): 103 mEq/L
2. Identify the sample size (\( n \)): 150
3. Identify the standard deviation (\( \sigma \)): 44 mEq/L
4. Determine the confidence level (90%), which corresponds to a critical z-value (typically found using a z-table or statistical software).
The formula for the confidence interval is given by:
\[ \bar{x} \pm z \left( \frac{\sigma}{\sqrt{n}} \right) \]
Where:
- \( \bar{x} \) is the sample mean
- \( z \) is the z-value corresponding to the desired confidence level
- \( \sigma \) is the population standard deviation
- \( n \) is the sample size
5. Calculate the standard error (SE):
\[ SE = \frac{\sigma}{\sqrt{n}} \]
6. Use the critical z-value for a 90% confidence interval (which is approximately 1.645 for a two-tailed test).
7. Calculate the margin of error (ME):
\[ ME = z \times SE \]
8. Determine the lower and upper limits of the confidence interval:
\[ \text{Lower limit} = \bar{x} - ME \]
\[ \text{Upper limit} = \bar{x} + ME \]
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
##### Input Fields:
- **Lower limit:**
- **Upper limit:**
---
This educational problem involves calculating the confidence interval for the true mean chloride level in Colorado residents by using the known sample statistics. This exercise helps in understanding the application of confidence intervals in statistics, specifically for estimating population parameters.
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