An experiment was conducted to find out the strength of a certain type of braided cord after weathering. The strengths of 56 pieces of cord that had been weathered for 30 days were investigated. The 56 pieces of cord were placed simultaneously in a tensile strength device. The device applies an increasing amount of force until the cord fails.
These are the cord strengths:
19.7 21.6 21.9 23.5 24.2 24.4 24.9 25.1
26.4 26.9 27.6 27.7 27.9 28.4 29.8 30.7
31.1 31.1 31.7 31.8 32.6 34.0 34.8 34.9
35.1 36.6 37.0 37.7 38.7 38.7 39.0 39.6
40.0 41.4 41.4 41.8 42.2 43.5 44.5 45.0
45.5 45.9 46.3 46.7 46.7 47.0 47.0 47.4
47.6 48.6 48.8 57.9 58.3 67.9 84.2 97.3
Question:
The manufacturer is planning a sales campaign to promote its cord and would like to state a tensile strength value for its cord. Provide the manufacturer with a 95% confidence interval that would provide an estimate of the MEDIAN tensile strength value for the weathered braided cord.
In order to determine if the braided cord has tensile strength that falls within federal specifications, the manufacturer wants to determine an interval of strength values, (TL; TU), such that the manufacturer would be 95% confident that the interval would contain at least 90% of all strength values for its braided cords.