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 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.

3,965	4,864	4,876.	4,390	4,279	4,457
3,959	3,901	4,839	4,892	4,735	3,904

Answer 1

We have for given data ,

Sample size:12

Mean (x̄): 4421.75

Variance (s^2): 170901.6591

Standard deviation (s): 413.40254

Degree of freedom =n-1 = 12 - 1 = 11

Lower tail chi square critical value is 5.578.................by using Excel command CHIINV(1-(0.2/2),11)

Upper tail chi square critical value is 17.275..................by using Excel command CHIINV((0.2/2),11)

We can use here,

Therefore, we are 80% confident that the standard deviation of the duration times of game play is between 329.883 to 580.537