Q13. Twelve different video games showing substance use were observed and the duration of times of...

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Q13. Twelve different video games showing substance use wereobserved and the duration of times of game playâ€‹ (in seconds) arelisted below. The design of the study justifies the assumption thatthe sample can be treated as a simple random sample. Use the sampledata to construct an 80â€‹%
confidence interval estimate of
sigma Ïƒâ€‹,
the standard deviation of the duration times of game play.Assume that this sample was obtained from a population with anormal distribution.
4015
3995
4344 4981
4516â€ƒ
3971
3939
4236
4895
4146
3890
4971
The confidence interval estimate is nothing __?_sec lessthan
sec.
(Round to one decimal place asâ€‹ needed.)

Answer & Explanation Solved by verified expert

4.4 Ratings (917 Votes)

Sample Size,Â Â n=Â Â 12
Sample Standard Deviation,Â Â s = âˆš(Î£(X- xÌ… )Â²/(n-1) ) = 417.5571
Confidence Level,Â Â CL=Â Â 0.80
Â Â Â Â Â
Â Â Â Â Â
Degrees of Freedom,Â Â DF=n-1 = Â Â 11
alpha,Â Â Î±=1-CL=Â Â 0.2
alpha/2 ,Â Â Î±/2=Â Â 0.1
Lower Chi-Square Value=Â Â Ï‡Â²1-Î±/2 =Â Â 5.5778
Upper Chi-Square Value=Â Â Ï‡Â²Î±/2 =Â Â 17.2750
Â Â Â Â Â
confidence interval for variance isÂ Â Â Â Â
lower bound=Â Â (n-1)sÂ²/Ï‡Â²Î±/2 =Â Â 111021.24
Â Â Â Â Â
Â Â Â Â Â
upper bound=Â Â (n-1)sÂ²/Ï‡Â²1-Î±/2 =Â Â 343844.91
Â Â Â Â Â

confidence interval for population std dev is Â Â Â Â Â
lower bound=Â Â âˆš(lower bound variance)=Â Â 333.2
Â Â Â Â Â
upper bound=Â Â âˆš(upper bound of variance=Â Â 586.4

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