The number of hours of reserve capacity of 10 randomly selected automotive batteries is shown to the right. 1.71 1.85 1.56 1.66 1.79 1.91 1.35 1.51 1.45 2.01 Assume the sample is taken from a normally distributed population. Construct 95% confidence intervals for (a) the population variance o and (b) the population standard deviation o. (a) The confidence interval for the population variance is ( ). (Round to three decimal places as needed.)
The number of hours of reserve capacity of 10 randomly selected automotive batteries is shown to the right. 1.71 1.85 1.56 1.66 1.79 1.91 1.35 1.51 1.45 2.01 Assume the sample is taken from a normally distributed population. Construct 95% confidence intervals for (a) the population variance o and (b) the population standard deviation o. (a) The confidence interval for the population variance is ( ). (Round to three decimal places as needed.)
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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Answer parts a and b
![**Educational Website Content:**
### Constructing Confidence Intervals for Population Variance and Standard Deviation
The following exercise explores the concept of constructing 95% confidence intervals for both the population variance \( \sigma^2 \) and the population standard deviation \( \sigma \).
#### Data Description:
The scenario involves the reserve capacity (in hours) of 10 randomly selected automotive batteries. The reserve capacities recorded are as follows:
- **1.71, 1.85, 1.56, 1.66, 1.79**
- **1.91, 1.35, 1.51, 1.45, 2.01**
#### Task:
Assume the given sample is taken from a normally distributed population. You are required to construct the 95% confidence intervals for:
- (a) The population variance \( \sigma^2 \)
- (b) The population standard deviation \( \sigma \)
**(a)** The confidence interval for the population variance is \( [ \_\_\_ , \_\_\_ ] \).
*Note: Round your final answers to three decimal places.*
This exercise helps in understanding practical applications of statistical concepts in estimating the range within which a population parameter lies with a given level of confidence.
#### Reminder:
- To construct these intervals, standard statistical methods and formulas, potentially involving chi-square distributions, are employed.
- Ensure accurate calculation and attention to rounding instructions for precise results.
For further assistance, feel free to explore more resources or examples related to confidence interval computation on our educational site.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69841bf7-b9f0-4fc9-8153-6ebe52f9298f%2Fad576f93-6803-43d1-9c31-698501563656%2Fs47p74m.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content:**
### Constructing Confidence Intervals for Population Variance and Standard Deviation
The following exercise explores the concept of constructing 95% confidence intervals for both the population variance \( \sigma^2 \) and the population standard deviation \( \sigma \).
#### Data Description:
The scenario involves the reserve capacity (in hours) of 10 randomly selected automotive batteries. The reserve capacities recorded are as follows:
- **1.71, 1.85, 1.56, 1.66, 1.79**
- **1.91, 1.35, 1.51, 1.45, 2.01**
#### Task:
Assume the given sample is taken from a normally distributed population. You are required to construct the 95% confidence intervals for:
- (a) The population variance \( \sigma^2 \)
- (b) The population standard deviation \( \sigma \)
**(a)** The confidence interval for the population variance is \( [ \_\_\_ , \_\_\_ ] \).
*Note: Round your final answers to three decimal places.*
This exercise helps in understanding practical applications of statistical concepts in estimating the range within which a population parameter lies with a given level of confidence.
#### Reminder:
- To construct these intervals, standard statistical methods and formulas, potentially involving chi-square distributions, are employed.
- Ensure accurate calculation and attention to rounding instructions for precise results.
For further assistance, feel free to explore more resources or examples related to confidence interval computation on our educational site.
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