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.

4,608 4,760 3,816 3,867 4,572 3,913

4,751 5,009 4,312 3,858 4,493 4,413

Answer 1

Suppose, random variable X denotes duration (in seconds) of times of game play.

Corresponding statistic is given by

Here,

Sample size

Sample variance

Degrees of freedom

We know,

[Using R-code 'qchisq((1-0.80)/2,11)' and 'qchisq(1-(1-0.80)/2,11)']

Hence, 80% confidence interval estimate of , standard deviation of duration is (327.593, 576.518).