Stats Question

Question

Twelve different video games showing substance use were observed and the duration times of game play (in seconds) are listed below (based on data from “Content and Ratings of Teen-Rated Video Games,” by Haninger and Thompson, Journal of the American Medical Association, Vol. 291, No. 7). The design of the study justifies the assumption that the sample can be treated as a simple random sample.  4049 3884 3859 4027 4318 4813 4657 4033 5004 4823 4334 4317

 

A) Use the sample data to construct a 95% confidence interval estimate of μ, the mean duration of game play.

 

B) Use the sample data to construct a 99% confidence interval estimate of σ, the standard deviation of the duration times of game play.

Answer 1

From data set, we can calculate: n=12; ∑=52118; Xbar=4343.2; S=394.91

(A)

For 95%CL margin of error: Z_a/2*(S/√n)

For critical value, Z_a/2: 0.95/2 = 0.475...  look-up in z-value table... 1.96

For StndError, S/√n: 394.91/√12 = 114.00

Margin of error = 1.96*114=±223.44

∴ 95CI limits of mean are: Xbar-223.44 & Xbar+223.44

4119.73 to 4566.61  (my answer might be slightly off due to decimal place value truncation)

(B)

For above stated S, n, & StndError and 99%CL...

99CI limits of standard deviation are: 253.21 to 811.789

 

NOTE:  You can use calculators from various statistical tools to calculate the above.  Formulas are also available in books, in case you want the classic approach. :-)  I hope I did not confuse or misunderstand your question...if I did, apologies in advance.  Thanks!

 

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