Question

# twelve different video games showing substance use were observed and the duration times of game play...

twelve different video games showing substance use were observed and the duration 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 data to construct a 95% confidence interval estimate of μ, the mean duration of game play.

4058 3879 3856 4027 4039 4822 4666 4029 5014 4825 4330 4319

• Here Let X1 be the random variable denoting the duration of game play
• The mean and variance is given by
• Mean =4322
• sample standard deviation is given by
• =408.5836
• To calculate the 95% confidence interval for the duration is given by
• The criticle value for Za/2=Z0.025 for t distribution is for 11 degrees of freedom is given by 2.201
• 0.95=P(-2.201<t(0.025,11)<2.201)
• 0.95=P(-2.201<<2.201)
• margin of error
• criticle value* standard error=2.201*(408.58/sqrt(10))=284.56
• Hence by substituting the calculated values the confidence interval is given by
• (4037<<4606)