Twelve different video games showing substance use were observed and the duration of times of game play (in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. Use the sample data to construct a 90% confidence interval estimate of o, the standard deviation of the duration times of game play. Assume that this sample was obtained from a population with a normal distribution. 4,252 4,820 4,150 4,921 4,008 4,782 4,156 4,852 4,348 3,895 4,710 4,377 Click the icon to view the table of Chi-Square critical values. The confidence interval estimate is sec
Twelve different video games showing substance use were observed and the duration of times of game play (in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. Use the sample data to construct a 90% confidence interval estimate of o, the standard deviation of the duration times of game play. Assume that this sample was obtained from a population with a normal distribution. 4,252 4,820 4,150 4,921 4,008 4,782 4,156 4,852 4,348 3,895 4,710 4,377 Click the icon to view the table of Chi-Square critical values. The confidence interval estimate is sec
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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![### Confidence Interval for Standard Deviation of Game Play Duration
**Objective:**
Evaluate the standard deviation of the duration times of gameplay (in seconds) using a 90% confidence interval based on a sample.
**Scenario:**
Twelve different video games that showcase substance use were observed. The duration of gameplay times (in seconds) is listed below. The study assumes that the sample can be considered as a simple random sample and is normally distributed.
**Gameplay Duration Times (in seconds):**
| Game | Times 1 | Times 2 |
|------|---------|---------|
| 1 | 4,252 | 4,156 |
| 2 | 4,820 | 4,852 |
| 3 | 4,150 | 4,348 |
| 4 | 4,921 | 3,895 |
| 5 | 4,008 | 4,710 |
| 6 | 4,782 | 4,377 |
**Steps to Construct the 90% Confidence Interval:**
1. Use the sample data to calculate the sample variance (s²).
2. Find the Chi-Square critical values for the 90% confidence level with degrees of freedom (df = n-1), where n is the number of observations.
3. Apply the formula for the confidence interval for the population variance (σ²):
\[
\left( \frac{(n-1) s^2}{\chi^2_{\alpha/2}}, \frac{(n-1) s^2}{\chi^2_{1-\alpha/2}} \right)
\]
4. Take the square root of the upper and lower bounds of the confidence interval for the variance to get the interval for the standard deviation (σ).
**Chi-Square Critical Values:**
- Click on the icon to view the table of Chi-Square critical values (if available).
**Confidence Interval Calculation:**
- Compute the sample variance based on the provided data.
- Use the Chi-Square critical values for a 90% confidence interval.
- Calculate and round off the confidence interval estimate for the standard deviation (σ) to one decimal place as needed.
**Results:**
- The confidence interval estimate for the standard deviation (σ) should be in the form of:
\[
\text{Confidence](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd231b9ce-fd1e-4b68-9592-c0bb04fbf540%2F9b6ebf31-bb25-42c9-9e6b-f4db18b821c5%2Fzjw2odg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Confidence Interval for Standard Deviation of Game Play Duration
**Objective:**
Evaluate the standard deviation of the duration times of gameplay (in seconds) using a 90% confidence interval based on a sample.
**Scenario:**
Twelve different video games that showcase substance use were observed. The duration of gameplay times (in seconds) is listed below. The study assumes that the sample can be considered as a simple random sample and is normally distributed.
**Gameplay Duration Times (in seconds):**
| Game | Times 1 | Times 2 |
|------|---------|---------|
| 1 | 4,252 | 4,156 |
| 2 | 4,820 | 4,852 |
| 3 | 4,150 | 4,348 |
| 4 | 4,921 | 3,895 |
| 5 | 4,008 | 4,710 |
| 6 | 4,782 | 4,377 |
**Steps to Construct the 90% Confidence Interval:**
1. Use the sample data to calculate the sample variance (s²).
2. Find the Chi-Square critical values for the 90% confidence level with degrees of freedom (df = n-1), where n is the number of observations.
3. Apply the formula for the confidence interval for the population variance (σ²):
\[
\left( \frac{(n-1) s^2}{\chi^2_{\alpha/2}}, \frac{(n-1) s^2}{\chi^2_{1-\alpha/2}} \right)
\]
4. Take the square root of the upper and lower bounds of the confidence interval for the variance to get the interval for the standard deviation (σ).
**Chi-Square Critical Values:**
- Click on the icon to view the table of Chi-Square critical values (if available).
**Confidence Interval Calculation:**
- Compute the sample variance based on the provided data.
- Use the Chi-Square critical values for a 90% confidence interval.
- Calculate and round off the confidence interval estimate for the standard deviation (σ) to one decimal place as needed.
**Results:**
- The confidence interval estimate for the standard deviation (σ) should be in the form of:
\[
\text{Confidence
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