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 the data to construct a 90% confidence interval estimate of µ, the mean duration of game play.
What is the confidence interval estimate of the population mean µ ? __ < µ < __ (round to one decimal place as needed)
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Get the mean, mu = sum of values divided by number of values, n
Get the variance = sum (value-mean)^2/(n-1) get the standard deviation s.d. = sqrt(variance)
Get the standard error of the mean from s.e. = s.d./sqrt(n)
Assume a normal (Gaussian) distribution approximately for means.
Check table of Gaussian distribuiotn to find how many +- s.e. you need to include 90% of the values. For example +- 2 s.e includes 95% of values.
Interpretation: means are more nearly Gaussian than underlying distributions from which they come, and 90% of the true means would be expected to lie within +- k s.d. of the sample mean, if only random error.