Use the given information to find the number of degrees of freedom, the critical values X and XR, and the assume that a simple random sample has been selected from a population with a normal distribution. Platelet Counts of Women 90% confidence; n = 40, s = 65.9. Click the icon to view the table of Chi-Square critical values. df=(Type a whole number.) x²-0 (Round to three decimal places as needed.). x² = 0 (Round to three decimal places as needed.) is << The confidence interval estimate of a is ***
Use the given information to find the number of degrees of freedom, the critical values X and XR, and the assume that a simple random sample has been selected from a population with a normal distribution. Platelet Counts of Women 90% confidence; n = 40, s = 65.9. Click the icon to view the table of Chi-Square critical values. df=(Type a whole number.) x²-0 (Round to three decimal places as needed.). x² = 0 (Round to three decimal places as needed.) is << The confidence interval estimate of a is ***
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Chi-Square Distribution Analysis for Platelet Counts**
To determine the confidence interval for a population standard deviation based on a sample, the following steps and information are essential:
1. **Sample Information**:
- **Confidence Level**: 90%
- **Sample Size (n)**: 40
- **Sample Standard Deviation (s)**: 65.9
2. **Objective**:
- Calculate the degrees of freedom.
- Identify the critical values for the Chi-Square distribution.
- Estimate the confidence interval for the population standard deviation (σ).
3. **Calculations**:
- **Degrees of Freedom (df)**:
\[
\text{df} = n - 1
\]
- Input a whole number for degrees of freedom.
- **Chi-Square Critical Values**:
- \( \chi^2_L \) (Lower critical value)
- \( \chi^2_R \) (Upper critical value)
- Round these values to three decimal places.
4. **Confidence Interval for σ**:
- The interval is represented as:
\[
\left( \frac{\sqrt{df} \cdot s}{\sqrt{\chi^2_R}} \right) < \sigma < \left( \frac{\sqrt{df} \cdot s}{\sqrt{\chi^2_L}} \right)
\]
- Ensure accurate rounding for your final calculation.
Use the Chi-Square critical value table to find the necessary values and complete the analysis. This method assumes the sample originates from a normally distributed population.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38d7ad60-cd84-472c-8996-4a82bb3a3198%2F59b5f835-7e3e-4130-8d05-825e1aee5501%2Fj1olwvi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Chi-Square Distribution Analysis for Platelet Counts**
To determine the confidence interval for a population standard deviation based on a sample, the following steps and information are essential:
1. **Sample Information**:
- **Confidence Level**: 90%
- **Sample Size (n)**: 40
- **Sample Standard Deviation (s)**: 65.9
2. **Objective**:
- Calculate the degrees of freedom.
- Identify the critical values for the Chi-Square distribution.
- Estimate the confidence interval for the population standard deviation (σ).
3. **Calculations**:
- **Degrees of Freedom (df)**:
\[
\text{df} = n - 1
\]
- Input a whole number for degrees of freedom.
- **Chi-Square Critical Values**:
- \( \chi^2_L \) (Lower critical value)
- \( \chi^2_R \) (Upper critical value)
- Round these values to three decimal places.
4. **Confidence Interval for σ**:
- The interval is represented as:
\[
\left( \frac{\sqrt{df} \cdot s}{\sqrt{\chi^2_R}} \right) < \sigma < \left( \frac{\sqrt{df} \cdot s}{\sqrt{\chi^2_L}} \right)
\]
- Ensure accurate rounding for your final calculation.
Use the Chi-Square critical value table to find the necessary values and complete the analysis. This method assumes the sample originates from a normally distributed population.
Expert Solution

Step 1
Step by step
Solved in 2 steps

Recommended textbooks for you

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

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
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON

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
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman