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

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Statistics

Q13. Twelve different video games showing substance use wereobserved and the duration of times of game play​ (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 80​%

confidence interval estimate of

sigma σ​,

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

4015

3995

43444981

4516 

3971

3939

4236

4895

4146

3890

4971

The confidence interval estimate is nothing __?_sec lessthan

sec.

(Round to one decimal place as​ needed.)

Answer & Explanation Solved by verified expert
4.4 Ratings (917 Votes)

Sample Size,   n=   12
Sample Standard Deviation,   s = √(Σ(X- x̅ )²/(n-1) ) = 417.5571
Confidence Level,   CL=   0.80
      
      
Degrees of Freedom,   DF=n-1 =    11
alpha,   α=1-CL=   0.2
alpha/2 ,   α/2=   0.1
Lower Chi-Square Value=   χ²1-α/2 =   5.5778
Upper Chi-Square Value=   χ²α/2 =   17.2750
      
confidence interval for variance is      
lower bound=   (n-1)s²/χ²α/2 =   111021.24
      
      
upper bound=   (n-1)s²/χ²1-α/2 =   343844.91
      

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

      
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