Question

Twelve different video games showing substance use were observed and the duration of 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 sample data to construct a 99​% confidence interval estimate of sigma​, the standard deviation of the duration times of game play. Assume that this sample was obtained from a population with a normal distribution. 4811 4751 4268 4096 3887 4182 4808 4266 4541 4993 4540 4196 The confidence interval estimate is ?

Answer 1

We have for given data,                                          
                                              
Sample variance =118691.902                                      
Sample standard deviation=344.517                              
Sample size =12                                      
                                              
Degree of freedom =n-1=   11                                  
Level of significance given =1-0.99=0.01                                  
Chi square critical value for lower tail=2.603                          
                                              
Chi square critical value for upper tail=26.757                          
                                              
We can use here confidence interval formula for population standard deviation

=(220.897,708.192)
                      
                                              
Lower confidence limit for population standard deviation=220.897                  
                                              
Upper confidence limit for Population standard deviation=708.192