According to the article “Fatigue Testing of Condoms”

(Polymer Testing, 2009: 567–571), “tests currently used for t.005,40 t.05,40 t.05,25 t.05,15 t.1,15 condoms are surrogates for the challenges they face in use,”

including a test for holes, an inflation test, a package seal test, and tests of dimensions and lubricant quality (all fertile territory for the use of statistical methodology!). The investigators developed a new test that adds cyclic strain to a level well below breakage and determines the number of cycles to break. A sample of 20 condoms of one particular type resulted in a sample mean number of 1584 and a sample standard deviation of 607.

Calculate and interpret a confidence interval at the 99% confidence level for the true average number of cycles to break. [Note: The article presented the results of hypothesis tests based on the t distribution; the validity of these depends on assuming normal population distributions.]