Homework Help is Here – Start Your Trial Now!
Math
Statistics
## Statistical Analysis of Blended Fuels Concerns about climate change and CO₂ reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 46 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. ### Problem Statement **(a)** If the true mean is 0.9660 with a standard deviation of 0.0060, within what interval will 98 percent of the sample means fall? (Round your answers to 4 decimal places.) **The interval is from ____ to ____** **(b)** If the true mean is 0.9660 with a standard deviation of 0.0060, what is the sampling distribution of \(\bar{X}\)? 1. Exactly normal with \(\mu = 0.9660\) and \(\sigma = 0.0060\). 2. Approximately normal with \(\mu = 0.9660\) and \(\sigma = 0.0060\). 3. Exactly normal with \(\mu = 0.9660\) and \(\sigma_{\bar{X}} = 0.0060/\sqrt{46}\). 4. Approximately normal with \(\mu = 0.9660\) and \(\sigma_{\bar{X}} = 0.0060/\sqrt{46}\). ### Explanation of Concepts - **True Mean (\(\mu\))**: The average value expected in the population. - **Standard Deviation (\(\sigma\))**: A measure of variability or dispersion of a set of values. - **Sampling Distribution of \(\bar{X}\)**: The probability distribution of the sample mean across different samples. ### Educational Insight Understanding the distribution of sample means helps in predicting the behavior of averages from samples, crucial for quality control and hypothesis testing in the context of fuel blends. This example highlights the application of statistical concepts in assessing environmental impacts and making informed decisions in fuel production.

## Statistical Analysis of Blended Fuels Concerns about climate change and CO₂ reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 46 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. ### Problem Statement **(a)** If the true mean is 0.9660 with a standard deviation of 0.0060, within what interval will 98 percent of the sample means fall? (Round your answers to 4 decimal places.) **The interval is from ____ to ____** **(b)** If the true mean is 0.9660 with a standard deviation of 0.0060, what is the sampling distribution of \(\bar{X}\)? 1. Exactly normal with \(\mu = 0.9660\) and \(\sigma = 0.0060\). 2. Approximately normal with \(\mu = 0.9660\) and \(\sigma = 0.0060\). 3. Exactly normal with \(\mu = 0.9660\) and \(\sigma_{\bar{X}} = 0.0060/\sqrt{46}\). 4. Approximately normal with \(\mu = 0.9660\) and \(\sigma_{\bar{X}} = 0.0060/\sqrt{46}\). ### Explanation of Concepts - **True Mean (\(\mu\))**: The average value expected in the population. - **Standard Deviation (\(\sigma\))**: A measure of variability or dispersion of a set of values. - **Sampling Distribution of \(\bar{X}\)**: The probability distribution of the sample mean across different samples. ### Educational Insight Understanding the distribution of sample means helps in predicting the behavior of averages from samples, crucial for quality control and hypothesis testing in the context of fuel blends. This example highlights the application of statistical concepts in assessing environmental impacts and making informed decisions in fuel production.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
## Statistical Analysis of Blended Fuels Concerns about climate change and CO₂ reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 46 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. ### Problem Statement **(a)** If the true mean is 0.9660 with a standard deviation of 0.0060, within what interval will 98 percent of the sample means fall? (Round your answers to 4 decimal places.) **The interval is from ____ to ____** **(b)** If the true mean is 0.9660 with a standard deviation of 0.0060, what is the sampling distribution of \(\bar{X}\)? 1. Exactly normal with \(\mu = 0.9660\) and \(\sigma = 0.0060\). 2. Approximately normal with \(\mu = 0.9660\) and \(\sigma = 0.0060\). 3. Exactly normal with \(\mu = 0.9660\) and \(\sigma_{\bar{X}} = 0.0060/\sqrt{46}\). 4. Approximately normal with \(\mu = 0.9660\) and \(\sigma_{\bar{X}} = 0.0060/\sqrt{46}\). ### Explanation of Concepts - **True Mean (\(\mu\))**: The average value expected in the population. - **Standard Deviation (\(\sigma\))**: A measure of variability or dispersion of a set of values. - **Sampling Distribution of \(\bar{X}\)**: The probability distribution of the sample mean across different samples. ### Educational Insight Understanding the distribution of sample means helps in predicting the behavior of averages from samples, crucial for quality control and hypothesis testing in the context of fuel blends. This example highlights the application of statistical concepts in assessing environmental impacts and making informed decisions in fuel production.
Transcribed Image Text:## Statistical Analysis of Blended Fuels Concerns about climate change and CO₂ reduction have initiated the commercial production of blends of biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 46 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. ### Problem Statement **(a)** If the true mean is 0.9660 with a standard deviation of 0.0060, within what interval will 98 percent of the sample means fall? (Round your answers to 4 decimal places.) **The interval is from ____ to ____** **(b)** If the true mean is 0.9660 with a standard deviation of 0.0060, what is the sampling distribution of \(\bar{X}\)? 1. Exactly normal with \(\mu = 0.9660\) and \(\sigma = 0.0060\). 2. Approximately normal with \(\mu = 0.9660\) and \(\sigma = 0.0060\). 3. Exactly normal with \(\mu = 0.9660\) and \(\sigma_{\bar{X}} = 0.0060/\sqrt{46}\). 4. Approximately normal with \(\mu = 0.9660\) and \(\sigma_{\bar{X}} = 0.0060/\sqrt{46}\). ### Explanation of Concepts - **True Mean (\(\mu\))**: The average value expected in the population. - **Standard Deviation (\(\sigma\))**: A measure of variability or dispersion of a set of values. - **Sampling Distribution of \(\bar{X}\)**: The probability distribution of the sample mean across different samples. ### Educational Insight Understanding the distribution of sample means helps in predicting the behavior of averages from samples, crucial for quality control and hypothesis testing in the context of fuel blends. This example highlights the application of statistical concepts in assessing environmental impacts and making informed decisions in fuel production.
Expert Solution
Step 1

The given values are

The sample mean= X =0.9660

The sample size =n= 46

Standard deviation =  σ = 0.00060

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS