Statistics

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

4040
3884
3859
4033
4308
4815
4663
4036
5012
4824
4332
4321

What is the confidence interval estimate of the population mean?

Answer 1

Hello,

 

Most confidence intervals can be computed using the following formula:

 

M ± t*SE

Where M is the mean of the sample, t is the t critical value and SE is the standard error of the mean.

 

For your sample, the mean is 4343.917.

 

The t critical value can be found using the normal distribution table (your teacher should have given you one or there should be one in your textbook). We need to find the t value that corresponds with an alpha level of 1% (or 0.01) and 11 degrees of freedom (12 participants minus 1). I will assume your teacher wants the 2-tailed (non-directional) value. Using the t table, we see that this value is 3.106.

 

The standard error equals the standard deviation divided by the square root of the sample size. The standard deviation of your sample is 396.922 and the sample size is 12. This gives us a standard error of 114.58. Now we can just plug everything in.

 

4343.917 + 3.106*114.58 = 4699.81

4343.917 - 3.106*114.58 = 3988.03

 

So the 99% confidence interval is 3988.03 to 4699.81