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 sigma​, the standard deviation of the duration times of game play. Assume that this sample was obtained from a population with a normal distribution.

4671, 3809 ,4019, 4217, 3823, 4892, 4534, 4450, 3902, 4430. 3874 4891

Answer 1

∑x = 51512

∑x² = 222949082

n = 12

Standard deviation, s = √[(Ʃx² - (Ʃx)²/n)/(n-1)] = √[(222949082-(51512)²/12)/(12-1)] = 407.3458

95% Confidence interval for population standard deviation :

Critical value, χ²α/2 = CHISQ.INV.RT(0.05/2, 11) = 21.9200

Critical value, χ²1-α/2 = CHISQ.INV.RT(1-0.05/2, 11) = 3.8157

Lower Bound = √((n-1)s²/χ²α/2) = √((12 - 1)407.3458/21.92) = 288.5618

Upper Bound = √((n-1)s²/χ²1-α/2) = √((12 - 1)407.3458/3.8157) = 691.6235