Use the sample data to construct a 95​% confidence interval estimate of σ​, the standard deviation of the duration times of game play

Question

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 95​% 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

4,803	3,903	3,914	4,351	4,325	4,033
4,097	4,290	4,439	4,454	3,806	4,298

The confidence interval estimate is

Answer 1

s = 285.553834546557

(n-1)s²/σ² ~ Χ²₁₁

The 95% probability of the chi-squared distribution is (3.8157482522361, 21.9200492610212)

Then, the 95% CI for σ² is (11 * s^2/21.9200492610212, 11 * s^2/21.9200492610212) =

(11 * 285.553834546557^2/21.9200492610212, 11 * 285.553834546557^2/21.9200492610212) =

(40919.2016854473, 235065.538231207)

and the 95% CI for σ is

( 202.284951702907, 484.835578553397)