An experiment was conducted to find out the strength of certain type of braided cord after weathering. The strengths of 56 pieces of cord which had been weathered for 30 days were investigated. The 56 pieces of cord were placed at the same time in a tensile strength device. The device applies an increasing amount of force till 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 the sales campaign to promote its cord as well as would like to state a tensile strength value for its cord. Give the manufacturer with a 95% confidence interval which would provide an estimate of the MEDIAN tensile strength value for the weathered braided cord.
In order to find out if the braided cord has tensile strength that falls in federal specifications, the manufacturer wants to find out an interval of strength values, (TL; TU), such that the manufacturer would be 95% confident that the interval would have at least 90% of all strength values for its braided cords.