0) Construct a 98% confidence interval for the population mean, u. Assume the population has a normal distribution. A study of 14 car owners showed that their average repair bill was $192 with a standard deviation of $8. Round to the nearest cent.
0) Construct a 98% confidence interval for the population mean, u. Assume the population has a normal distribution. A study of 14 car owners showed that their average repair bill was $192 with a standard deviation of $8. Round to the nearest cent.
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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would like to know if this can be found on stat crunch if it can be
![**Task 10: Confidence Interval Calculation**
Construct a 98% confidence interval for the population mean, \( \mu \). Assume the population has a normal distribution. A study of 14 car owners showed that their average repair bill was $192 with a standard deviation of $8. Round to the nearest cent.
**Explanation for Students:**
- **Population Mean (\( \mu \))**: The true average of all possible repair bills in the population.
- **Sample Size**: 14 car owners.
- **Sample Mean**: $192.
- **Standard Deviation**: $8.
- **Confidence Level**: 98%, which indicates how confident we are that the interval contains the population mean.
**Instructions:**
1. **Identify the Z-Score:** For a 98% confidence level, refer to a Z-table to find the Z-score that corresponds to the upper and lower 1% of the probability distribution.
2. **Calculate the Margin of Error (ME):**
\[
ME = Z \times \left(\frac{\text{Standard Deviation}}{\sqrt{\text{Sample Size}}}\right)
\]
3. **Compute the Confidence Interval:**
\[
\text{Confidence Interval} = \text{Sample Mean} \pm ME
\]
Use the above steps to find the 98% confidence interval for the average repair bill of car owners in the population.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca98936e-33c7-4402-95ae-aeafe8e3f8b8%2F49991547-93d5-42ae-b786-43a52b84fab9%2Fd9mlvu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Task 10: Confidence Interval Calculation**
Construct a 98% confidence interval for the population mean, \( \mu \). Assume the population has a normal distribution. A study of 14 car owners showed that their average repair bill was $192 with a standard deviation of $8. Round to the nearest cent.
**Explanation for Students:**
- **Population Mean (\( \mu \))**: The true average of all possible repair bills in the population.
- **Sample Size**: 14 car owners.
- **Sample Mean**: $192.
- **Standard Deviation**: $8.
- **Confidence Level**: 98%, which indicates how confident we are that the interval contains the population mean.
**Instructions:**
1. **Identify the Z-Score:** For a 98% confidence level, refer to a Z-table to find the Z-score that corresponds to the upper and lower 1% of the probability distribution.
2. **Calculate the Margin of Error (ME):**
\[
ME = Z \times \left(\frac{\text{Standard Deviation}}{\sqrt{\text{Sample Size}}}\right)
\]
3. **Compute the Confidence Interval:**
\[
\text{Confidence Interval} = \text{Sample Mean} \pm ME
\]
Use the above steps to find the 98% confidence interval for the average repair bill of car owners in the population.
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