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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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Question
q46
![**Title: Statistical Analysis of Steel Rod Lengths**
**Introduction:**
A manufacturing plant produces steel rods. During one production run of 20,000 such rods, the specifications called for rods that were 46 cm in length and 3.8 cm in width. Fifteen of these rods, comprising a random sample, were measured for length. The resulting measurements are presented below. This data will be used to estimate the population variance of length for the rods. It is assumed that rod length is normally distributed in the population. A 99% confidence interval will be constructed, and the ramifications of the results will be discussed.
**Sample Measurements:**
- 44 cm
- 47 cm
- 43 cm
- 46 cm
- 46 cm
- 45 cm
- 43 cm
- 44 cm
- 47 cm
- 46 cm
- 48 cm
- 48 cm
- 43 cm
- 44 cm
- 45 cm
**Statistical Task:**
Construct a 99% confidence interval for the population variance of the rod lengths. Use these measurements to complete the analysis. The final confidence interval should be rounded to two decimal places.
**Solution Format:**
\[
\text{Confidence Interval: } \square \leq \sigma^2 \leq \square
\]
**Instructions:**
1. Calculate the sample mean and variance.
2. Use the Chi-Square distribution to find the critical values.
3. Construct the confidence interval around the sample variance.
4. Discuss the potential implications for production quality and control.
**Note:**
Round all final answers to two decimal places, as shown in the example (e.g., 1.75).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ff8a9d1-27d7-4c01-984f-c0979e8297f8%2F7c97a369-5088-4552-b5f0-593aa288ac1c%2F9pb2rvg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Statistical Analysis of Steel Rod Lengths**
**Introduction:**
A manufacturing plant produces steel rods. During one production run of 20,000 such rods, the specifications called for rods that were 46 cm in length and 3.8 cm in width. Fifteen of these rods, comprising a random sample, were measured for length. The resulting measurements are presented below. This data will be used to estimate the population variance of length for the rods. It is assumed that rod length is normally distributed in the population. A 99% confidence interval will be constructed, and the ramifications of the results will be discussed.
**Sample Measurements:**
- 44 cm
- 47 cm
- 43 cm
- 46 cm
- 46 cm
- 45 cm
- 43 cm
- 44 cm
- 47 cm
- 46 cm
- 48 cm
- 48 cm
- 43 cm
- 44 cm
- 45 cm
**Statistical Task:**
Construct a 99% confidence interval for the population variance of the rod lengths. Use these measurements to complete the analysis. The final confidence interval should be rounded to two decimal places.
**Solution Format:**
\[
\text{Confidence Interval: } \square \leq \sigma^2 \leq \square
\]
**Instructions:**
1. Calculate the sample mean and variance.
2. Use the Chi-Square distribution to find the critical values.
3. Construct the confidence interval around the sample variance.
4. Discuss the potential implications for production quality and control.
**Note:**
Round all final answers to two decimal places, as shown in the example (e.g., 1.75).
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