Twelve different video games showing substance use were obse

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 ?, the mean duration of game play.

4044
3890
3856
4036
4326
4822
4663
4030
5009
4817
4329
4319

What is the confidence interval estimate of the population mean ??

____<?< ____

(Round to one decimal place as needed.)

Solution

sample size=12

sample mean=4345.083

sample standard deviation=396.0118

The degree of freedom =n-1=12-1=11

Given a=1-0.9=0.1, t(0.05, df=11)=1.796 (from student t table)

So the lower bound is

xbar - t*s/vn =4345.083 - 1.796*396.0118/sqrt(12) =4139.8

So the upper bound is

xbar +t*s/vn =4345.083 + 1.796*396.0118/sqrt(12) =4550.4

Answer: 4139.8<?<4550.4