Question

According to the article "Fatigue Testing of Condoms" (Polymer Testing, 2009: 567–571), "tests currently used for 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.
1. 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.]

Answer 1

Answer:

99% Confidence interval:  (1196,1973)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 20

Mean, μ = 1584

Standard Deviation, σ = 607

99% Confidence interval:  

$\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}$  

Putting the values, we get,  

$t_{critical}\text{ at degree of freedom 19 and}~\alpha_{0.01} = \pm 2.86$  

$1584 \pm 2.86(\dfrac{607}{\sqrt{20}} )\\\\ = 1584 \pm 388.18\\ = (1195.82 ,1972.18)\\ \approx (1196,1973)$

Thus, there is a 99% chance that it will break in approximately 1196 to 1972