Question

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 95?% confidence interval estimate of ??, the mean duration of game play.

4053,

3881,

3851,

4037,

4319,

4808,

4664,

4038,

5013,

4819,

4327,

4326

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Answer 1

Solution :

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.

We have to use the data to construct a 95?% confidence interval estimate of ??, the mean duration of game play.

Since the sample size is 12 and the standard deviation is estimated from the random sample given , so we will make use of the t distribution critical value in the 95% Confidence Interval of ?.

We know , that the 100(1)% Confidence Interval of is given as ,

where , is the sample size ;   is the sample mean ;   is the sample standard deviation ;

is the level of significance ;   is the upper % point of the t distn with dfs.

Calculations :

From the given data , we have the following information ,

Thus , the 95% Confidence Interval for   is given as ,

  

  

  

Thus , the 95% Confidence Interval for   is given as [ 4093.27 , 4596.063 ] ........................ (Ans)