An experiment was conducted to find out the strength of a certain kind 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 concurrently in a tensile strength device. The device applies a rising 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
The manufacturer of the cord is planning some major changes to their cord which will amplify the tensile strength. After making alters in the product, it will be necessary to run a large study to validate that the changes have in fact increased the tensile strength. Find out the minimum sample size necessary to be at least 95% confident that the tensile strengths obtained in the sample will cover 90% of tensile strengths produced in the new manufacturing procedure.