Assume that a sample is used to estimate a population mean u. Find the 99% confidence interval for a sample of size 977 with a mean of 16.6 and a standard deviation of 15.6. Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). < µ < Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
Assume that a sample is used to estimate a population mean u. Find the 99% confidence interval for a sample of size 977 with a mean of 16.6 and a standard deviation of 15.6. Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). < µ < Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
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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![**Example Problem: Estimating a Population Mean**
Assume that a sample is used to estimate a population mean \( \mu \). Find the 99% confidence interval for a sample of size 977 with a mean of 16.6 and a standard deviation of 15.6. Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
\[ \text{[ ]} < \mu < \text{[ ]} \]
**Instructions:**
- Answer should be obtained without any preliminary rounding.
- However, the critical value may be rounded to 3 decimal places.
**Explanation:**
This problem involves calculating a confidence interval for a population mean from sample data. The interval provides a range of values within which the true population mean is likely to fall. This calculation assumes that the distribution of the sample mean is approximately normal due to the large sample size (Central Limit Theorem).
To solve this, you will need to:
1. Determine the critical value for a 99% confidence level.
2. Calculate the standard error of the mean.
3. Apply the formula for the confidence interval:
\[
\text{Confidence Interval} = \text{mean} \pm (\text{critical value} \times \text{standard error})
\]
Where:
- **Mean** = 16.6
- **Standard Deviation** = 15.6
- **Sample Size** = 977
Ensure all calculations maintain accuracy until the final answer, where the result will be rounded to one decimal place for reporting.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ebf9e4a-d88a-4068-a98e-7c5e269e8031%2F0a4c0459-3c9e-4c08-b1c3-d24bc047494e%2Fdimfio_processed.png&w=3840&q=75)
Transcribed Image Text:**Example Problem: Estimating a Population Mean**
Assume that a sample is used to estimate a population mean \( \mu \). Find the 99% confidence interval for a sample of size 977 with a mean of 16.6 and a standard deviation of 15.6. Enter your answer as a tri-linear inequality accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
\[ \text{[ ]} < \mu < \text{[ ]} \]
**Instructions:**
- Answer should be obtained without any preliminary rounding.
- However, the critical value may be rounded to 3 decimal places.
**Explanation:**
This problem involves calculating a confidence interval for a population mean from sample data. The interval provides a range of values within which the true population mean is likely to fall. This calculation assumes that the distribution of the sample mean is approximately normal due to the large sample size (Central Limit Theorem).
To solve this, you will need to:
1. Determine the critical value for a 99% confidence level.
2. Calculate the standard error of the mean.
3. Apply the formula for the confidence interval:
\[
\text{Confidence Interval} = \text{mean} \pm (\text{critical value} \times \text{standard error})
\]
Where:
- **Mean** = 16.6
- **Standard Deviation** = 15.6
- **Sample Size** = 977
Ensure all calculations maintain accuracy until the final answer, where the result will be rounded to one decimal place for reporting.
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