### Duration of Video Game Play Study#### Study OverviewTwelve different video games showing substance use were observed, and the durations of gameplay (in seconds) were recorded as follows:- 4,397 - 4,343 - 4,107 - 4,363 - 4,523 - 4,801 - 4,507 - 3,943 - 4,957 - 4,508 - 4,337 - 3,899 The study aims to justify the assumption that this sample can be treated as a simple random sample. Use the sample data to construct an 80% confidence interval estimate of σ, the standard deviation of the duration times of game play. Assume that this sample was obtained from a population with a normal distribution.#### Step-by-Step Solution1. **Data Collection**: The list of gameplay times above provides the raw data.2. **Statistical Assumption**: This data set assumes that the duration times follow a normal distribution which is a prerequisite for constructing a confidence interval for the standard deviation.3. **Confidence Interval Calculation**: - Calculate the sample mean and sample standard deviation. - Use the Chi-Square distribution to find the critical values. - Construct the confidence interval using these standard formulae: \[ \left( \frac{(n - 1) \cdot s^2}{\chi^2_{\text{upper}}}, \frac{(n - 1) \cdot s^2}{\chi^2_{\text{lower}}} \right) \] Where: - $n$ is the sample size, - $s^2$ is the sample variance, - $\chi^2_{\text{upper}}$ and $\chi^2_{\text{lower}}$ are the critical values from the Chi-Square distribution for the desired confidence level.To visualize and better understand the Chi-Square distribution, you can click the provided link in the original software or educational content to view the table of Chi-Square critical values.#### Result InterpretationAfter calculating the confidence interval:- The confidence interval estimate for the standard deviation is interpreted as the range where the true population standard deviation of gameplay durations likely falls. This interval is essential for making inferences about the expected variability in gameplay durations due to substance use depicted in the

Solution:- From given information x (x-x¯)2 4397 43.3398 4343 2248.3434 4107 80325.0258…

Answered: Twelve different video games showing…

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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