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 90% confidence interval estimate of the standard deviation of the duration times of game play. Assume that this sample was obtained from a population with a normal distribution 5.004 3.867 4678 3.829 4.515 4.609 4,517 4,841 Click the icon to view the table of Chemical values The confidence intervalovimate in all Round tone decimal place as needed)

Answer 1

X X - mean (X-mean)2 5.004 0.6233 0.3885 3.515 -0.8657 0.7494 3.887 -0.4937 0.2437 4.609 0.2283 0.0521 4.168 -0.2127 0.0452 4.654 0.2733 0.0747 4.446 0.0653 0.0043 4.517 0.1363 0.0186 4.678 0.2973 0.0884 4.42 0.0393 0.0015 3.829 -0.5517 0.3044 4.841 0.4603 0.2119 Variance(s) (Στη – ) n - 1 2 -C 2.1827 n = 12 2.1827 Variance(s) = 11 Variance(52) = 0.1984 Standard Deviation(s) Variance Standard Deviation(s) = 0.4454

First we find the confidence interval for variance

2 Xa/2,n-1 = X6.05.11 19.6751 Xi-a/2,4-1= 16.95, 11 4.5748 (n-1) s (n 1)s Confidence interval 2 xa/2,n-1 'Xi-a/2,n-1 (12 - 1)0.44542 (12 - 1)0.44542 Required confidence interval 19.6751 4.5748 (11)0.1984 (11)0.1984 Required confidence interval 19.6751 4.5748 Required confidence interval = (0.1109, 0.477) Taking the square root of the endpoints of this interval we obtain, Required confidence interval (0.333, 0.6907) 0.333 <o<0.6907

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